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This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

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A [[wp:Almost prime|k-Almost-prime]] is a natural number $n$ that is the product of $k$ (possibly identical) primes.

;Example: 1-almost-primes, where $k=1$, are the prime numbers themselves.

2-almost-primes, where $k=2$, are the [[Semiprime|semiprimes]].

;Task: Write a function/method/subroutine/... that generates k-almost primes and use it to create a table here of the first ten members of k-Almost primes for $1 <= K <= 5$.

• [[Semiprime]]
• [[:Category:Prime Numbers]]

## 11l

{{trans|Kotlin}}

```F k_prime(k, =n)
V f = 0
V p = 2
L f < k & p * p <= n
L n % p == 0
n /= p
f++
p++
R f + (I n > 1 {1} E 0) == k

F primes(k, n)
V i = 2
Array[Int] list
L list.len < n
I k_prime(k, i)
list.append(i)
i++
R list

L(k) 1..5
print(‘k = ’k‘: ’, end' ‘’)
print(primes(k, 10))
```

{{out}}

```k = 1: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
k = 2: [4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
k = 3: [8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
k = 4: [16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
k = 5: [32, 48, 72, 80, 108, 112, 120, 162, 168, 176]
```

This imports the package '''Prime_Numbers''' from [[Prime decomposition#Ada]].

```with Prime_Numbers, Ada.Text_IO;

procedure Test_Kth_Prime is

package Integer_Numbers is new
Prime_Numbers (Natural, 0, 1, 2);
use Integer_Numbers;

Out_Length: constant Positive := 10; -- 10 k-th almost primes
N: Positive; -- the "current number" to be checked

begin
for K in 1 .. 5 loop
Ada.Text_IO.Put("K =" & Integer'Image(K) &":  ");
N := 2;
for I in 1 .. Out_Length loop
while Decompose(N)'Length /= K loop
N := N + 1;
end loop; -- now N is Kth almost prime;
N := N + 1;
end loop;
end loop;
end Test_Kth_Prime;
```

{{output}} K = 1: 2 3 5 7 11 13 17 19 23 29 K = 2: 4 6 9 10 14 15 21 22 25 26 K = 3: 8 12 18 20 27 28 30 42 44 45 K = 4: 16 24 36 40 54 56 60 81 84 88 K = 5: 32 48 72 80 108 112 120 162 168 176

## ALGOL 68

Worth noticing is the n(...)(...) picture in the printf and the WHILE ... DO SKIP OD idiom which is quite common in ALgol 68.

```BEGIN
INT examples=10, classes=5;
MODE SEMIPRIME = STRUCT ([examples]INT data, INT count);
[classes]SEMIPRIME semi primes;
PROC num facs = (INT n) INT :
COMMENT
Return number of not necessarily distinct prime factors of n.
Not very efficient for large n ...
COMMENT
BEGIN
INT tf := 2, residue := n, count := 1;
WHILE tf < residue DO
INT remainder = residue MOD tf;
( remainder = 0 | count +:= 1; residue %:= tf | tf +:= 1 )
OD;
count
END;
PROC update table = (REF []SEMIPRIME table, INT i) BOOL :
COMMENT
Add i to the appropriate row of the table, if any, unless that row
is already full. Return a BOOL which is TRUE when all of the table
is full.
COMMENT
BEGIN
INT k := num facs(i);
IF k <= classes
THEN
INT c = 1 + count OF table[k];
( c <= examples | (data OF table[k])[c] := i; count OF table[k] := c )
FI;
INT sum := 0;
FOR i TO classes DO sum +:= count OF table[i] OD;
sum < classes * examples
END;
FOR i TO classes DO count OF semi primes[i] := 0 OD;
FOR i FROM 2 WHILE update table (semi primes, i) DO SKIP OD;
FOR i TO classes
DO
printf ((\$"k = ", d, ":", n(examples)(xg(0))l\$, i, data OF semi primes[i]))
OD
END
```

{{out}}

```k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176

```

## ARM Assembly

{{works with|as|Raspberry Pi}}

```
/* ARM assembly Raspberry PI  */
/*  program kprime.s   */

/************************************/
/* Constantes                       */
/************************************/
.equ STDOUT, 1     @ Linux output console
.equ EXIT,   1     @ Linux syscall
.equ WRITE,  4     @ Linux syscall

.equ MAXI,  10
.equ MAXIK,  5
/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessDeb:           .ascii "k="
sMessValeurDeb:     .fill 11, 1, ' '            @ size => 11

sMessResult:        .ascii " "
sMessValeur:        .fill 11, 1, ' '            @ size => 11

szCarriageReturn:   .asciz "\n"

/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                                             @ entry of program
mov r3,#1                                     @ k
1:                                                @ start loop k
mov r0,r3
bl conversion10                               @ call conversion decimal
mov r1,#':'
strb r1,[r0,#2]                               @ write : after k value
mov r1,#0
strb r1,[r0,#3]                               @ final zéro
bl affichageMess                              @ display message
mov r4,#2                                     @ n
mov r5,#0                                     @ result counter
2:                                                @ start loop n
mov r0,r4
mov r1,r3
bl kprime                                     @ is kprine ?
cmp r0,#0
beq 3f                                        @ no
mov r0,r4
bl conversion10                               @ call conversion decimal
mov r1,#0
strb r1,[r0,#4]                               @ final zéro
bl affichageMess                              @ display message
3:
cmp r5,#MAXI                                  @ maxi ?
blt 2b                                        @ no -> loop
bl affichageMess                              @ display carriage return
cmp r3,#MAXIK                                 @ maxi ?
ble 1b                                        @ no -> loop

100:                                              @ standard end of the program
mov r0, #0                                    @ return code
mov r7, #EXIT                                 @ request to exit program
svc #0                                        @ perform the system call

/******************************************************************/
/*     compute kprime (n,k)                                       */
/******************************************************************/
/* r0 contains n */
/* r1 contains k */
kprime:
push {r1-r7,lr}                                   @ save  registers
mov r5,r0                                         @ save n
mov r7,r1                                         @ save k
mov r4,#0                                         @ counter product
mov r1,#2                                         @ divisor
1:                                                    @ start loop
cmp r4,r7                                         @ counter >= k
bge 4f                                            @ yes -> end
mul r6,r1,r1                                      @ compute product
cmp r6,r5                                         @ > n
bgt 4f                                            @ yes -> end
2:                                                    @ start loop division
mov r0,r5                                         @ dividende
bl division                                       @ by r1
cmp r3,#0                                         @ remainder = 0 ?
bne 3f                                            @ no
mov r5,r2                                         @ yes -> n = n / r1
b 2b                                              @ and loop
3:
b 1b                                              @ and loop
4:                                                    @ end compute
cmp r5,#1                                         @ n > 1
addgt r4,#1                                       @ yes increment counter
cmp r4,r7                                         @ counter = k ?
movne r0,#0                                       @ no -> no kprime
moveq r0,#1                                       @ yes -> kprime
100:
pop {r1-r7,lr}                                    @ restaur registers
bx lr                                             @return
/******************************************************************/
/*     display text with size calculation                         */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {r0,r1,r2,r7,lr}                          @ save  registres
mov r2,#0                                      @ counter length
1:                                                 @ loop length calculation
ldrb r1,[r0,r2]                                @ read octet start position + index
cmp r1,#0                                      @ if 0 its over
bne 1b                                         @ and loop
@ so here r2 contains the length of the message
mov r1,r0                                      @ address message in r1
mov r0,#STDOUT                                 @ code to write to the standard output Linux
mov r7, #WRITE                                 @ code call system "write"
svc #0                                         @ call systeme
pop {r0,r1,r2,r7,lr}                           @ restaur des  2 registres */
bx lr                                          @ return
/******************************************************************/
/*     Converting a register to a decimal unsigned                */
/******************************************************************/
/* r0 contains value and r1 address area   */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes          */
.equ LGZONECAL,   10
conversion10:
push {r1-r4,lr}                                 @ save registers
mov r3,r1
mov r2,#LGZONECAL
1:                                                  @ start loop
bl divisionpar10U                               @ unsigned  r0 <- dividende. quotient ->r0 reste -> r1
strb r1,[r3,r2]                                 @ store digit on area
cmp r0,#0                                       @ stop if quotient = 0
subne r2,#1                                     @ else previous position
bne 1b                                          @ and loop
@ and move digit from left of area
mov r4,#0
2:
ldrb r1,[r3,r2]
strb r1,[r3,r4]
cmp r2,#LGZONECAL
ble 2b
@ and move spaces in end on area
mov r0,r4                                         @ result length
mov r1,#' '                                       @ space
3:
strb r1,[r3,r4]                                   @ store space in area
cmp r4,#LGZONECAL
ble 3b                                            @ loop if r4 <= area size

100:
pop {r1-r4,lr}                                    @ restaur registres
bx lr                                             @return

/***************************************************/
/*   division par 10   unsigned                    */
/***************************************************/
/* r0 dividende   */
/* r0 quotient    */
/* r1 remainder   */
divisionpar10U:
push {r2,r3,r4, lr}
mov r4,r0                                          @ save value
ldr r3,iMagicNumber                                @ r3 <- magic_number    raspberry 1 2
umull r1, r2, r3, r0                               @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0)
mov r0, r2, LSR #3                                 @ r2 <- r2 >> shift 3
add r2,r0,r0, lsl #2                               @ r2 <- r0 * 5
sub r1,r4,r2, lsl #1                               @ r1 <- r4 - (r2 * 2)  = r4 - (r0 * 10)
pop {r2,r3,r4,lr}
bx lr                                              @ leave function
iMagicNumber:  	.int 0xCCCCCCCD
/***************************************************/
/* integer division unsigned                       */
/***************************************************/
division:
/* r0 contains dividend */
/* r1 contains divisor */
/* r2 returns quotient */
/* r3 returns remainder */
push {r4, lr}
mov r2, #0                                         @ init quotient
mov r3, #0                                         @ init remainder
mov r4, #32                                        @ init counter bits
b 2f
1:                                                     @ loop
movs r0, r0, LSL #1                                @ r0 <- r0 << 1 updating cpsr (sets C if 31st bit of r0 was 1)
adc r3, r3, r3                                     @ r3 <- r3 + r3 + C. This is equivalent to r3 ? (r3 << 1) + C
cmp r3, r1                                         @ compute r3 - r1 and update cpsr
subhs r3, r3, r1                                   @ if r3 >= r1 (C=1) then r3 <- r3 - r1
adc r2, r2, r2                                     @ r2 <- r2 + r2 + C. This is equivalent to r2 <- (r2 << 1) + C
2:
subs r4, r4, #1                                    @ r4 <- r4 - 1
bpl 1b                                             @ if r4 >= 0 (N=0) then loop
pop {r4, lr}
bx lr

```

Output:

```
k=1 : 2    3    5    7    11   13   17   19   23   29
k=2 : 4    6    9    10   14   15   21   22   25   26
k=3 : 8    12   18   20   27   28   30   42   44   45
k=4 : 16   24   36   40   54   56   60   81   84   88
k=5 : 32   48   72   80   108  112  120  162  168  176

```

## AutoHotkey

Translation of the C Version

```kprime(n,k) {
p:=2, f:=0
while( (f<k) && (p*p<=n) ) {
while ( 0==mod(n,p) ) {
n/=p
f++
}
p++
}
return f + (n>1) == k
}

k:=1, results:=""
while( k<=5 ) {
i:=2, c:=0, results:=results "k =" k ":"
while( c<10 ) {
if (kprime(i,k)) {
results:=results " " i
c++
}
i++
}
results:=results "`n"
k++
}

MsgBox % results
```

'''Output (Msgbox):'''

```k =1: 2 3 5 7 11 13 17 19 23 29
k =2: 4 6 9 10 14 15 21 22 25 26
k =3: 8 12 18 20 27 28 30 42 44 45
k =4: 16 24 36 40 54 56 60 81 84 88
k =5: 32 48 72 80 108 112 120 162 168 176
```

## AWK

```
# syntax: GAWK -f ALMOST_PRIME.AWK
BEGIN {
for (k=1; k<=5; k++) {
printf("%d:",k)
c = 0
i = 1
while (c < 10) {
if (kprime(++i,k)) {
printf(" %d",i)
c++
}
}
printf("\n")
}
exit(0)
}
function kprime(n,k,  f,p) {
for (p=2; f<k && p*p<=n; p++) {
while (n % p == 0) {
n /= p
f++
}
}
return(f + (n > 1) == k)
}

```

Output:

```
1: 2 3 5 7 11 13 17 19 23 29
2: 4 6 9 10 14 15 21 22 25 26
3: 8 12 18 20 27 28 30 42 44 45
4: 16 24 36 40 54 56 60 81 84 88
5: 32 48 72 80 108 112 120 162 168 176

```

## Befunge

{{trans|C}} The extra spaces are to ensure it's readable on buggy interpreters that don't include a space after numeric output.

```::48*"= k",,,,02p.":",01v
|^ v0!`\*:g40:<p402p300:+1<
K| >2g03g`*#v_ 1`03g+02g->|
F@>/03g1+03p>vpv+1\.:,*48 <
P#|!\g40%g40:<4>:9`>#v_\1^|
|^>#!1#`+#50#:^#+1,+5>#5\$<|
```

{{out}}

```k = 1 : 2  3  5  7  11  13  17  19  23  29
k = 2 : 4  6  9  10  14  15  21  22  25  26
k = 3 : 8  12  18  20  27  28  30  42  44  45
k = 4 : 16  24  36  40  54  56  60  81  84  88
k = 5 : 32  48  72  80  108  112  120  162  168  176
```

## C

```#include <stdio.h>

int kprime(int n, int k)
{
int p, f = 0;
for (p = 2; f < k && p*p <= n; p++)
while (0 == n % p)
n /= p, f++;

return f + (n > 1) == k;
}

int main(void)
{
int i, c, k;

for (k = 1; k <= 5; k++) {
printf("k = %d:", k);

for (i = 2, c = 0; c < 10; i++)
if (kprime(i, k)) {
printf(" %d", i);
c++;
}

putchar('\n');
}

return 0;
}
```

{{out}}

```
k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176

```

## C++

{{trans|Kotlin}}

```#include <cstdlib>
#include <iostream>
#include <sstream>
#include <iomanip>
#include <list>

bool k_prime(unsigned n, unsigned k) {
unsigned f = 0;
for (unsigned p = 2; f < k && p * p <= n; p++)
while (0 == n % p) { n /= p; f++; }
return f + (n > 1 ? 1 : 0) == k;
}

std::list<unsigned> primes(unsigned k, unsigned n)  {
std::list<unsigned> list;
for (unsigned i = 2;list.size() < n;i++)
if (k_prime(i, k)) list.push_back(i);
return list;
}

int main(const int argc, const char* argv[]) {
using namespace std;
for (unsigned k = 1; k <= 5; k++) {
ostringstream os("");
const list<unsigned> l = primes(k, 10);
for (list<unsigned>::const_iterator i = l.begin(); i != l.end(); i++)
os << setw(4) << *i;
cout << "k = " << k << ':' << os.str() << endl;
}

return EXIT_SUCCESS;
}
```

{{out}}

```k = 1:   2   3   5   7  11  13  17  19  23  29
k = 2:   4   6   9  10  14  15  21  22  25  26
k = 3:   8  12  18  20  27  28  30  42  44  45
k = 4:  16  24  36  40  54  56  60  81  84  88
k = 5:  32  48  72  80 108 112 120 162 168 176
```

## C#

```using System;
using System.Collections.Generic;
using System.Linq;

namespace AlmostPrime
{
class Program
{
static void Main(string[] args)
{
foreach (int k in Enumerable.Range(1, 5))
{
KPrime kprime = new KPrime() { K = k };
Console.WriteLine("k = {0}: {1}",
k, string.Join<int>(" ", kprime.GetFirstN(10)));
}
}
}

class KPrime
{
public int K { get; set; }

public bool IsKPrime(int number)
{
int primes = 0;
for (int p = 2; p * p <= number && primes < K; ++p)
{
while (number % p == 0 && primes < K)
{
number /= p;
++primes;
}
}
if (number > 1)
{
++primes;
}
return primes == K;
}

public List<int> GetFirstN(int n)
{
List<int> result = new List<int>();
for (int number = 2; result.Count < n; ++number)
{
if (IsKPrime(number))
{
}
}
return result;
}
}
}
```

{{out}}

```
k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176

```

## Clojure

```

(ns clojure.examples.almostprime
(:gen-class))

(defn divisors [n]
" Finds divisors by looping through integers 2, 3,...i.. up to sqrt (n) [note: rather than compute sqrt(), test with i*i <=n] "
(let [div (some #(if (= 0 (mod n %)) % nil) (take-while #(<= (* % %) n) (iterate inc 2)))]
(if div                                                         ; div = nil (if no divisor found else its the divisor)
(into [] (concat (divisors div) (divisors (/ n div))))      ; Concat the two divisors of the two divisors
[n])))                                                      ; Number is prime so only itself as a divisor

(defn divisors-k [k n]
" Finds n numbers with k divisors.  Does this by looping through integers 2, 3, ... filtering (passing) ones with k divisors and
taking the first n "
(->> (iterate inc 2)            ; infinite sequence of numbers starting at 2
(map divisors)             ; compute divisor of each element of sequence
(filter #(= (count %) k))  ; filter to take only elements with k divisors
(take n)                   ; take n elements from filtered sequence
(map #(apply * %))))       ; compute number by taking product of divisors

(println (for [k (range 1 6)]
(println "k:" k (divisors-k k 10))))

}
```

{{out}}

```
(k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176)
nil

```

## Common Lisp

```(defun start ()
(loop for k from 1 to 5
do (format t "k = ~a: ~a~%" k (collect-k-almost-prime k))))

(defun collect-k-almost-prime (k &optional (d 2) (lst nil))
(cond ((= (length lst) 10) (reverse lst))
((= (?-primality d) k) (collect-k-almost-prime k (+ d 1) (cons d lst)))
(t (collect-k-almost-prime k (+ d 1) lst))))

(defun ?-primality (n &optional (d 2) (c 0))
(cond ((> d (isqrt n)) (+ c 1))
((zerop (rem n d)) (?-primality (/ n d) d (+ c 1)))
(t (?-primality n (+ d 1) c))))
```

{{out}}

```
k = 1: (2 3 5 7 11 13 17 19 23 29)
k = 2: (4 6 9 10 14 15 21 22 25 26)
k = 3: (8 12 18 20 27 28 30 42 44 45)
k = 4: (16 24 36 40 54 56 60 81 84 88)
k = 5: (32 48 72 80 108 112 120 162 168 176)
NIL
```

## D

This contains a copy of the function `decompose` from the Prime decomposition task. {{trans|Ada}}

```import std.stdio, std.algorithm, std.traits;

Unqual!T[] decompose(T)(in T number) pure nothrow
in {
assert(number > 1);
} body {
typeof(return) result;
Unqual!T n = number;

for (Unqual!T i = 2; n % i == 0; n /= i)
result ~= i;
for (Unqual!T i = 3; n >= i * i; i += 2)
for (; n % i == 0; n /= i)
result ~= i;

if (n != 1)
result ~= n;
return result;
}

void main() {
enum outLength = 10; // 10 k-th almost primes.

foreach (immutable k; 1 .. 6) {
writef("K = %d: ", k);
auto n = 2; // The "current number" to be checked.
foreach (immutable i; 1 .. outLength + 1) {
while (n.decompose.length != k)
n++;
// Now n is K-th almost prime.
write(n, " ");
n++;
}
writeln;
}
}
```

{{out}}

```K = 1: 2 3 5 7 11 13 17 19 23 29
K = 2: 4 6 9 10 14 15 21 22 25 26
K = 3: 8 12 18 20 27 28 30 42 44 45
K = 4: 16 24 36 40 54 56 60 81 84 88
K = 5: 32 48 72 80 108 112 120 162 168 176
```

## Delphi

{{trans|C}}

```
program AlmostPrime;

{\$APPTYPE CONSOLE}

function IsKPrime(const n, k: Integer): Boolean;
var
p, f, v: Integer;
begin
f := 0;
p := 2;
v := n;
while (f < k) and (p*p <= n) do begin
while (v mod p) = 0 do begin
v := v div p;
Inc(f);
end;
Inc(p);
end;
if v > 1 then Inc(f);
Result := f = k;
end;

var
i, c, k: Integer;

begin
for k := 1 to 5 do begin
Write('k = ', k, ':');
c := 0;
i := 2;
while c < 10 do begin
if IsKPrime(i, k) then begin
Write(' ', i);
Inc(c);
end;
Inc(i);
end;
WriteLn;
end;
end.

```

{{out}}

```K = 1: 2 3 5 7 11 13 17 19 23 29
K = 2: 4 6 9 10 14 15 21 22 25 26
K = 3: 8 12 18 20 27 28 30 42 44 45
K = 4: 16 24 36 40 54 56 60 81 84 88
K = 5: 32 48 72 80 108 112 120 162 168 176

```

## EchoLisp

Small numbers : filter the sequence [ 2 .. n]

```
(define (almost-prime? p k)
(= k (length (prime-factors p))))

(define (almost-primes k nmax)
(take (filter (rcurry almost-prime? k) [2 ..]) nmax))

(define (task (kmax 6) (nmax 10))
(for ((k [1 .. kmax]))
(write 'k= k '|)
(for-each write (almost-primes k nmax))
(writeln)))

```

{{out}}

```

k= 1 | 2 3 5 7 11 13 17 19 23 29
k= 2 | 4 6 9 10 14 15 21 22 25 26
k= 3 | 8 12 18 20 27 28 30 42 44 45
k= 4 | 16 24 36 40 54 56 60 81 84 88
k= 5 | 32 48 72 80 108 112 120 162 168 176

```

Large numbers : generate - combinations with repetitions - k-almost-primes up to pmax.

```
(lib 'match)
(define-syntax-rule (: v i) (vector-ref v i))
(reader-infix ':) ;; abbrev (vector-ref v i) === [v : i]

(lib 'bigint)
(define cprimes (list->vector (primes 10000)))

;; generates next k-almost-prime < pmax
;; c = vector of k primes indices c[i] <= c[j]
;; p = vector of intermediate products prime[c[0]]*prime[c[1]]*..
;; p[k-1] is the generated k-almost-prime
;; increment one c[i] at each step

(define (almost-next pmax k c p)
(define almost-prime #f)
(define cp 0)

(for ((i (in-range (1- k) -1 -1))) ;; look backwards for c[i] to increment
(vector-set! c i (1+ [c : i])) ;; increment c[i]
(set! cp [cprimes : [c : i]])
(vector-set! p i (if (> i 0) (* [ p : (1- i)] cp) cp)) ;; update partial product

(when (< [p : i) pmax)
(set! almost-prime
(and  ;; set followers to c[i] value
(for ((j (in-range (1+ i) k)))
(vector-set! c j [c : i])
(vector-set! p j (*  [ p : (1- j)] cp))
#:break (>= [p : j] pmax) => #f )
[p  : (1- k)]
) ;; // and
) ;; set!
) ;; when
#:break almost-prime
) ;; // for i
almost-prime )

;; not sorted list of k-almost-primes < pmax
(define (almost-primes k nmax)
(define base (expt 2 k)) ;; first one is 2^k
(define pmax (* base nmax))
(define c (make-vector k #0))
(define p (build-vector k (lambda(i) (expt #2 (1+ i)))))

(cons base
(for/list
((almost-prime (in-producer almost-next pmax k c p )))
almost-prime)))

```

{{out}}

```
;; we want  500-almost-primes from the 10000-th.
(take (drop (list-sort < (almost-primes 500 10000)) 10000 ) 10)

(7241149198492252834202927258094752774597239286103014697435725917649659974371690699721153852986
440733637405206125678822081264723636566725108094369093648384
etc ...

;; The first one is 2^497 * 3 * 17 * 347 , same result as Haskell.

```

## Elixir

{{trans|Erlang}}

```defmodule Factors do
def factors(n), do: factors(n,2,[])

defp factors(1,_,acc), do: acc
defp factors(n,k,acc) when rem(n,k)==0, do: factors(div(n,k),k,[k|acc])
defp factors(n,k,acc)                 , do: factors(n,k+1,acc)

def kfactors(n,k), do: kfactors(n,k,1,1,[])

defp kfactors(_tn,tk,_n,k,_acc) when k == tk+1, do: IO.puts "done! "
defp kfactors(tn,tk,_n,k,acc) when length(acc) == tn do
IO.puts "K: #{k} #{inspect acc}"
kfactors(tn,tk,2,k+1,[])
end
defp kfactors(tn,tk,n,k,acc) do
case length(factors(n)) do
^k -> kfactors(tn,tk,n+1,k,acc++[n])
_  -> kfactors(tn,tk,n+1,k,acc)
end
end
end

Factors.kfactors(10,5)
```

{{out}}

```
K: 1 [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
K: 2 [4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
K: 3 [8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
K: 4 [16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
K: 5 [32, 48, 72, 80, 108, 112, 120, 162, 168, 176]
done!
```

## Erlang

Using the factors function from [[Prime_decomposition#Erlang]].

```
-module(factors).
-export([factors/1,kfactors/0,kfactors/2]).

factors(N) ->
factors(N,2,[]).

factors(1,_,Acc) -> Acc;
factors(N,K,Acc) when N rem K == 0 ->
factors(N div K,K, [K|Acc]);
factors(N,K,Acc) ->
factors(N,K+1,Acc).

kfactors() -> kfactors(10,5,1,1,[]).
kfactors(N,K) -> kfactors(N,K,1,1,[]).
kfactors(_Tn,Tk,_N,K,_Acc) when K == Tk+1 ->  io:fwrite("Done! ");
kfactors(Tn,Tk,N,K,Acc) when length(Acc) == Tn  ->
io:format("K: ~w ~w ~n", [K, Acc]),
kfactors(Tn,Tk,2,K+1,[]);

kfactors(Tn,Tk,N,K,Acc) ->
case length(factors(N)) of K ->
kfactors(Tn,Tk, N+1,K, Acc ++ [ N ] );
_ ->
kfactors(Tn,Tk, N+1,K, Acc) end.

```

{{out}}

```
9> factors:kfactors(10,5).
K: 1 [2,3,5,7,11,13,17,19,23,29]
K: 2 [4,6,9,10,14,15,21,22,25,26]
K: 3 [8,12,18,20,27,28,30,42,44,45]
K: 4 [16,24,36,40,54,56,60,81,84,88]
K: 5 [32,48,72,80,108,112,120,162,168,176]
Done! ok
10> factors:kfactors(15,10).
K: 1 [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]
K: 2 [4,6,9,10,14,15,21,22,25,26,33,34,35,38,39]
K: 3 [8,12,18,20,27,28,30,42,44,45,50,52,63,66,68]
K: 4 [16,24,36,40,54,56,60,81,84,88,90,100,104,126,132]
K: 5 [32,48,72,80,108,112,120,162,168,176,180,200,208,243,252]
K: 6 [64,96,144,160,216,224,240,324,336,352,360,400,416,486,504]
K: 7 [128,192,288,320,432,448,480,648,672,704,720,800,832,972,1008]
K: 8 [256,384,576,640,864,896,960,1296,1344,1408,1440,1600,1664,1944,2016]
K: 9 [512,768,1152,1280,1728,1792,1920,2592,2688,2816,2880,3200,3328,3888,4032]
K: 10 [1024,1536,2304,2560,3456,3584,3840,5184,5376,5632,5760,6400,6656,7776,8064]
Done! ok

```

## ERRE

```
PROGRAM ALMOST_PRIME

!
! for rosettacode.org
!

!\$INTEGER

PROCEDURE KPRIME(N,K->KP)
LOCAL P,F
FOR P=2 TO 999 DO
EXIT IF NOT((F<K) AND (P*P<=N))
WHILE (N MOD P)=0 DO
N/=P
F+=1
END WHILE
END FOR
KP=(F-(N>1)=K)
END PROCEDURE

BEGIN
PRINT(CHR\$(12);)  !CLS
FOR K=1 TO 5 DO
PRINT("k =";K;":";)
C=0
FOR I=2 TO 999 DO
EXIT IF NOT(C<10)
KPRIME(I,K->KP)
IF KP THEN
PRINT(I;)
C+=1
END IF
END FOR
PRINT
END FOR
END PROGRAM

```

{{out}}

```K = 1: 2  3  5  7  11  13  17  19  23  29
K = 2: 4  6  9  10  14  15  21  22  25  26
K = 3: 8  12  18  20  27  28  30  42  44  45
K = 4: 16  24  36  40  54  56  60  81  84  88
K = 5: 32  48  72  80  108  112  120  162  168  176
```

## Factor

```USING: formatting fry kernel lists lists.lazy locals
math.combinatorics math.primes.factors math.ranges sequences ;
IN: rosetta-code.almost-prime

: k-almost-prime? ( n k -- ? )
'[ factors _ <combinations> [ product ] map ]
[ [ = ] curry ] bi any? ;

:: first10 ( k -- seq )
10 0 lfrom [ k k-almost-prime? ] lfilter ltake list>array ;

5 [1,b] [ dup first10 "K = %d: %[%3d, %]\n" printf ] each
```

{{out}}

```
K = 1: {   2,   3,   5,   7,  11,  13,  17,  19,  23,  29 }
K = 2: {   4,   6,   9,  10,  14,  15,  21,  22,  25,  26 }
K = 3: {   8,  12,  18,  20,  27,  28,  30,  42,  44,  45 }
K = 4: {  16,  24,  36,  40,  54,  56,  60,  81,  84,  88 }
K = 5: {  32,  48,  72,  80, 108, 112, 120, 162, 168, 176 }

```

## FreeBASIC

```' FB 1.05.0 Win64

Function kPrime(n As Integer, k As Integer) As Boolean
Dim f As Integer = 0
For i As Integer = 2 To n
While n Mod i = 0
If f = k Then Return false
f += 1
n \= i
Wend
Next
Return f = k
End Function

Dim As Integer i, c, k
For k = 1 To 5
Print "k = "; k; " : ";
i = 2
c = 0
While c < 10
If kPrime(i, k) Then
Print Using "### "; i;
c += 1
End If
i += 1
Wend
Print
Next

Print
Print "Press any key to quit"
Sleep
```

{{out}}

```
k =  1 :   2   3   5   7  11  13  17  19  23  29
k =  2 :   4   6   9  10  14  15  21  22  25  26
k =  3 :   8  12  18  20  27  28  30  42  44  45
k =  4 :  16  24  36  40  54  56  60  81  84  88
k =  5 :  32  48  72  80 108 112 120 162 168 176

```

## Frink

```for k = 1 to 5
{
n=2
count = 0
print["k=\$k:"]
do
{
if length[factorFlat[n]] == k
{
print[" \$n"]
count = count + 1
}
n = n + 1
} while count < 10

println[]
}
```

Output:

```
k=1: 2 3 5 7 11 13 17 19 23 29
k=2: 4 6 9 10 14 15 21 22 25 26
k=3: 8 12 18 20 27 28 30 42 44 45
k=4: 16 24 36 40 54 56 60 81 84 88
k=5: 32 48 72 80 108 112 120 162 168 176

```

## Futhark

```
let kprime(n: i32, k: i32): bool =
let (p,f) = (2, 0)
let (n,_,f) = loop (n, p, f) while f < k && p*p <= n do
let (n,f) = loop (n, f) while 0 == n % p do
(n/p, f+1)
in (n, p+1, f)
in f + (if n > 1 then 1 else 0) == k

let main(m: i32): [][]i32 =
let f k =
let ps = replicate 10 0
let (_,_,ps) = loop (i,c,ps) = (2,0,ps) while c < 10 do
if kprime(i,k) then
unsafe let ps[c] = i
in (i+1, c+1, ps)
else (i+1, c, ps)
in ps
in map f (1...m)

```

```let rec genFactor (f, n) =
if f > n then None
elif n % f = 0 then Some (f, (f, n/f))
else genFactor (f+1, n)

let factorsOf (num) =
Seq.unfold (fun (f, n) -> genFactor (f, n)) (2, num)

let kFactors k = Seq.unfold (fun n ->
let rec loop m =
if Seq.length (factorsOf m) = k then m
else loop (m+1)
let next = loop n
Some(next, next+1)) 2

[1 .. 5]
|> List.iter (fun k ->
printfn "%A" (Seq.take 10 (kFactors k) |> Seq.toList))
```

{{out}}

```[2; 3; 5; 7; 11; 13; 17; 19; 23; 29]
[4; 6; 9; 10; 14; 15; 21; 22; 25; 26]
[8; 12; 18; 20; 27; 28; 30; 42; 44; 45]
[16; 24; 36; 40; 54; 56; 60; 81; 84; 88]
[32; 48; 72; 80; 108; 112; 120; 162; 168; 176]
```

```package main

import "fmt"

func kPrime(n, k int) bool {
nf := 0
for i := 2; i <= n; i++ {
for n%i == 0 {
if nf == k {
return false
}
nf++
n /= i
}
}
return nf == k
}

func gen(k, n int) []int {
r := make([]int, n)
n = 2
for i := range r {
for !kPrime(n, k) {
n++
}
r[i] = n
n++
}
return r
}

func main() {
for k := 1; k <= 5; k++ {
fmt.Println(k, gen(k, 10))
}
}
```

{{out}}

```
1 [2 3 5 7 11 13 17 19 23 29]
2 [4 6 9 10 14 15 21 22 25 26]
3 [8 12 18 20 27 28 30 42 44 45]
4 [16 24 36 40 54 56 60 81 84 88]
5 [32 48 72 80 108 112 120 162 168 176]

```

## Groovy

```
public class almostprime
{
public static boolean kprime(int n,int k)
{
int i,div=0;
for(i=2;(i*i <= n) && (div<k);i++)
{
while(n%i==0)
{
n = n/i;
div++;
}
}
return div + ((n > 1)?1:0) == k;
}
public static void main(String[] args)
{
int i,l,k;
for(k=1;k<=5;k++)
{
println("k = " + k + ":");
l = 0;
for(i=2;l<10;i++)
{
if(kprime(i,k))
{
print(i + " ");
l++;
}
}
println();
}
}
}​

```

{{out}}

```
k = 1:
2 3 5 7 11 13 17 19 23 29
k = 2:
4 6 9 10 14 15 21 22 25 26
k = 3:
8 12 18 20 27 28 30 42 44 45
k = 4:
16 24 36 40 54 56 60 81 84 88
k = 5:
32 48 72 80 108 112 120 162 168 176

```

```
10  'Almost prime
20  FOR K% = 1 TO 5
30   PRINT "k = "; K%; ": ";
40   LET I% = 2
50   LET C% = 0
60   WHILE C% < 10
70    LET AN% = I%: LET AK% = K%: GOSUB 1000
80    IF ISKPRIME <> 0 THEN PRINT USING "### "; I%;: LET C% = C% + 1
90    LET I% = I% + 1
100  WEND
110  PRINT
120 NEXT K%
130 END

995  ' Check if n (AN%) is a k (AK%) prime
1000 LET F% = 0
1010 FOR II% = 2 TO AN%
1020  WHILE AN% MOD II% = 0
1030   IF F% = AK% THEN LET ISKPRIME = 0: RETURN
1040   LET F% = F% + 1
1050   LET AN% = AN% \ II%
1060  WEND
1070 NEXT II%
1080 LET ISKPRIME = (F% = AK%)
1090 RETURN

```

{{out}}

```
k =  1 :   2   3   5   7  11  13  17  19  23  29
k =  2 :   4   6   9  10  14  15  21  22  25  26
k =  3 :   8  12  18  20  27  28  30  42  44  45
k =  4 :  16  24  36  40  54  56  60  81  84  88
k =  5 :  32  48  72  80 108 112 120 162 168 176

```

``` a -> Bool
isPrime n = not \$ any ((0 ==) . (mod n)) [2..(truncate \$ sqrt \$ fromIntegral n)]

primes :: [Integer]
primes = filter isPrime [2..]

isKPrime :: (Num a, Eq a) => a -> Integer -> Bool
isKPrime 1 n = isPrime n
isKPrime k n = any (isKPrime (k - 1)) sprimes
where
sprimes = map fst \$ filter ((0 ==) . snd) \$ map (divMod n) \$ takeWhile (< n) primes

kPrimes :: (Num a, Eq a) => a -> [Integer]
kPrimes k = filter (isKPrime k) [2..]

main :: IO ()
main = flip mapM_ [1..5] \$ \k ->
putStrLn \$ "k = " ++ show k ++ ": " ++ (unwords \$ map show (take 10 \$ kPrimes k))
```

{{out}}

```k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176
```

Larger ''k''s require more complicated methods:

```primes = 2:3:[n | n <- [5,7..], foldr (\p r-> p*p > n || rem n p > 0 && r)
True (drop 1 primes)]

merge aa@(a:as) bb@(b:bs)
| a < b = a:merge as bb
| otherwise = b:merge aa bs

-- n-th item is all k-primes not divisible by any of the first n primes
notdivs k = f primes \$ kprimes (k-1) where
f (p:ps) s = map (p*) s : f ps (filter ((/=0).(`mod`p)) s)

kprimes k
| k == 1 = primes
| otherwise = f (head ndk) (tail ndk) (tail \$ map (^k) primes) where
ndk = notdivs k
-- tt is the thresholds for merging in next sequence
-- it is equal to "map head seqs", but don't do that
f aa@(a:as) seqs tt@(t:ts)
| a < t = a : f as seqs tt
| otherwise = f (merge aa \$ head seqs) (tail seqs) ts

main = do
-- next line is for task requirement:
mapM_ (\x->print (x, take 10 \$ kprimes x)) [1 .. 5]

putStrLn "\n10000th to 10100th 500-amost primes:"
mapM_ print \$ take 100 \$ drop 10000 \$ kprimes 500
```

{{out}}

```
(1,[2,3,5,7,11,13,17,19,23,29])
(2,[4,6,9,10,14,15,21,22,25,26])
(3,[8,12,18,20,27,28,30,42,44,45])
(4,[16,24,36,40,54,56,60,81,84,88])
(5,[32,48,72,80,108,112,120,162,168,176])

10000th to 10100th 500-amost primes:
7241149198492252834202927258094752774597239286103014697435725917649659974371690699721153852986440733637405206125678822081264723636566725108094369093648384
<...snipped 99 more equally unreadable numbers...>

```

Works in both languages.

```link "factors"

procedure main()
every writes(k := 1 to 5,": ") do
every writes(right(genKap(k),5)\10|"\n")
end

procedure genKap(k)
suspend (k = *factors(n := seq(q)), n)
end
```

Output:

```
->ap
1:     2    3    5    7   11   13   17   19   23   29
2:     4    6    9   10   14   15   21   22   25   26
3:     8   12   18   20   27   28   30   42   44   45
4:    16   24   36   40   54   56   60   81   84   88
5:    32   48   72   80  108  112  120  162  168  176
->

```

## J

```   (10 {. [:~.[:/:~[:,*/~)^:(i.5)~p:i.10
2  3  5  7  11  13  17  19  23  29
4  6  9 10  14  15  21  22  25  26
8 12 18 20  27  28  30  42  44  45
16 24 36 40  54  56  60  81  84  88
32 48 72 80 108 112 120 162 168 176
```

Explanation: #Generate 10 primes. #Multiply each of them by the first ten primes #Sort and find unique values, take the first ten of those #Multiply each of them by the first ten primes #Sort and find unique values, take the first ten of those :... The results of the odd steps in this procedure are the desired result.

## Java

```public class AlmostPrime {
public static void main(String[] args) {
for (int k = 1; k <= 5; k++) {
System.out.print("k = " + k + ":");

for (int i = 2, c = 0; c < 10; i++) {
if (kprime(i, k)) {
System.out.print(" " + i);
c++;
}
}

System.out.println("");
}
}

public static boolean kprime(int n, int k) {
int f = 0;
for (int p = 2; f < k && p * p <= n; p++) {
while (n % p == 0) {
n /= p;
f++;
}
}
return f + ((n > 1) ? 1 : 0) == k;
}
}
```

{{out}}

```
k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176

```

## Javascript

```function almostPrime (n, k) {
var divisor = 2, count = 0
while(count < k + 1 && n != 1) {
if (n % divisor == 0) {
n = n / divisor
count = count + 1
} else {
divisor++
}
}
return count == k
}

for (var k = 1; k <= 5; k++) {
document.write("
k=", k, ": ")
var count = 0, n = 0
while (count <= 10) {
n++
if (almostPrime(n, k)) {
document.write(n, " ")
count++
}
}
}
```

{{out}}

```
k=1: 2 3 5 7 11 13 17 19 23 29 31
k=2: 4 6 9 10 14 15 21 22 25 26 33
k=3: 8 12 18 20 27 28 30 42 44 45 50
k=4: 16 24 36 40 54 56 60 81 84 88 90
k=5: 32 48 72 80 108 112 120 162 168 176 180
```

## jq

{{Works with| jq|1.4}} '''Infrastructure:'''

```# Recent versions of jq (version > 1.4) have the following definition of "until":
def until(cond; next):
def _until:
if cond then . else (next|_until) end;
_until;

# relatively_prime(previous) tests whether the input integer is prime
# relative to the primes in the array "previous":
def relatively_prime(previous):
. as \$in
| (previous|length) as \$plen
# state: [found, ix]
|  [false, 0]
| until( .[0] or .[1] >= \$plen;
[ (\$in % previous[.[1]]) == 0, .[1] + 1] )
| .[0] | not ;

# Emit a stream in increasing order of all primes (from 2 onwards)
# that are less than or equal to mx:
def primes(mx):

# The helper function, next, has arity 0 for tail recursion optimization;
# it expects its input to be the array of previously found primes:
def next:
. as \$previous
| (\$previous | .[length-1]) as \$last
| if (\$last >= mx) then empty
else ((2 + \$last)
| until( relatively_prime(\$previous) ; . + 2)) as \$nextp
| if \$nextp <= mx
then \$nextp, (( \$previous + [\$nextp] ) | next)
else empty
end
end;
if mx <= 1 then empty
elif mx == 2 then 2
else (2, 3, ( [2,3] | next))
end
;

# Return an array of the distinct prime factors of . in increasing order
def prime_factors:

# Return an array of prime factors of . given that "primes"
# is an array of relevant primes:
def pf(primes):
if . <= 1 then []
else . as \$in
| if (\$in | relatively_prime(primes)) then [\$in]
else reduce primes[] as \$p
([];
if (\$in % \$p) != 0 then .
else . + [\$p] +  ((\$in / \$p) | pf(primes))
end)
end
| unique
end;

if . <= 1 then []
else . as \$in
| pf( [ primes( (1+\$in) | sqrt | floor)  ] )
end;

# Return an array of prime factors of . repeated according to their multiplicities:
def prime_factors_with_multiplicities:
# Emit p according to the multiplicity of p
# in the input integer assuming p > 1
def multiplicity(p):
if   .  < p     then empty
elif . == p     then p
elif (. % p) == 0 then
((./p) | recurse( if (. % p) == 0 then (. / p) else empty end) | p)
else empty
end;

if . <= 1 then []
else . as \$in
| prime_factors as \$primes
| if (\$in|relatively_prime(\$primes)) then [\$in]
else reduce \$primes[]  as \$p
([];
if (\$in % \$p) == 0 then . + [\$in|multiplicity(\$p)] else . end )
end
end;
```

'''isalmostprime'''

```def isalmostprime(k): (prime_factors_with_multiplicities | length) == k;

# Emit a stream of the first N almost-k primes
def almostprimes(N; k):
if N <= 0 then empty
else
[N, 1, null]
| recurse( if .[0] <= 0 then empty
elif (.[1] | isalmostprime(k)) then [.[0]-1, .[1]+1, .[1]]
else [.[0], .[1]+1, null]
end)
| .[2] | select(. != null)
end;
```

```range(1;6) as \$k | "k=\(\$k): \([almostprimes(10;\$k)])"
```

{{out}}

```\$ jq -c -r -n -f Almost_prime.jq
k=1: [2,3,5,7,11,13,17,19,23,29]
k=2: [4,6,9,10,14,15,21,22,25,26]
k=3: [8,12,18,20,27,28,30,42,44,45]
k=4: [16,24,36,40,54,56,60,81,84,88]
k=5: [32,48,72,80,108,112,120,162,168,176]
```

## Julia

{{works with|Julia|1.1}}

```using Primes

isalmostprime(n::Integer, k::Integer) = sum(values(factor(n))) == k

function almostprimes(N::Integer, k::Integer) # return first N almost-k primes
P = Vector{typeof(k)}(undef,N)
i = 0; n = 2
while i < N
if isalmostprime(n, k) P[i += 1] = n end
n += 1
end
return P
end

for k in 1:5
println("\$k-Almost-primes: ", join(almostprimes(10, k), ", "), "...")
end
```

{{out}}

```1-Almost-primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
2-Almost-primes: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26...
3-Almost-primes: 8, 12, 18, 20, 27, 28, 30, 42, 44, 45...
4-Almost-primes: 16, 24, 36, 40, 54, 56, 60, 81, 84, 88...
5-Almost-primes: 32, 48, 72, 80, 108, 112, 120, 162, 168, 176...
```

## Lua

```-- Returns boolean indicating whether n is k-almost prime
function almostPrime (n, k)
local divisor, count = 2, 0
while count < k + 1 and n ~= 1 do
if n % divisor == 0 then
n = n / divisor
count = count + 1
else
divisor = divisor + 1
end
end
return count == k
end

-- Generates table containing first ten k-almost primes for given k
function kList (k)
local n, kTab = 2^k, {}
while #kTab < 10 do
if almostPrime(n, k) then
table.insert(kTab, n)
end
n = n + 1
end
return kTab
end

-- Main procedure, displays results from five calls to kList()
for k = 1, 5 do
io.write("k=" .. k .. ": ")
for _, v in pairs(kList(k)) do
io.write(v .. ", ")
end
print("...")
end
```

{{out}}

```k=1: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...
k=2: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ...
k=3: 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, ...
k=4: 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, ...
k=5: 32, 48, 72, 80, 108, 112, 120, 162, 168, 176, ...
```

## Kotlin

{{trans|Java}}

```fun Int.k_prime(x: Int): Boolean {
var n = x
var f = 0
var p = 2
while (f < this && p * p <= n) {
while (0 == n % p) { n /= p; f++ }
p++
}
return f + (if (n > 1) 1 else 0) == this
}

fun Int.primes(n : Int) : List<Int> {
var i = 2
var list = mutableListOf<Int>()
while (list.size < n) {
i++
}
return list
}

fun main(args: Array<String>) {
for (k in 1..5)
println("k = \$k: " + k.primes(10))
}
```

{{out}}

```k = 1: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
k = 2: [4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
k = 3: [8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
k = 4: [16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
k = 5: [32, 48, 72, 80, 108, 112, 120, 162, 168, 176]
```

## Liberty BASIC

{{trans|FreeBASIC}} {{works with|Just BASIC}}

```
for k = 1 to 5
print "k = "; k; ": ";
i = 2
c = 0
while c < 10
if kPrime(i, k) then
print using("###", i); " ";
c = c + 1
end if
i = i + 1
wend
print
next k
end

function kPrime(n, k)
f = 0
for i = 2 to n
while n mod i = 0
if f = k then kPrime = 0: exit function
f = f + 1
n = int(n / i)
wend
next i
kPrime = abs(f = k)
end function

```

{{out}}

```
k = 1:   2   3   5   7  11  13  17  19  23  29
k = 2:   4   6   9  10  14  15  21  22  25  26
k = 3:   8  12  18  20  27  28  30  42  44  45
k = 4:  16  24  36  40  54  56  60  81  84  88
k = 5:  32  48  72  80 108 112 120 162 168 176

```

## Maple

```AlmostPrimes:=proc(k, numvalues::posint:=10)
local aprimes, i, intfactors;
aprimes := Array([]);
i := 0;

do
i := i + 1;
intfactors := ifactors(i)[2];
intfactors := [seq(seq(intfactors[i][1], j=1..intfactors[i][2]),i = 1..numelems(intfactors))];
if numelems(intfactors) = k then
ArrayTools:-Append(aprimes,i);
end if;
until numelems(aprimes) = 10:
aprimes;
end proc:
<seq( AlmostPrimes(i), i = 1..5 )>;
```

{{out}}

```
[[2, 3, 5, 7, 11, 13, 17, 19, 23, 29],
[4, 6, 9, 10, 14, 15, 21, 22, 25, 26],
[8, 12, 18, 20, 27, 28, 30, 42, 44, 45],
[16, 24, 36, 40, 54, 56, 60, 81, 84, 88],
[32, 48, 72, 80, 108, 112, 120, 162, 168, 176]]
```

```kprimes[k_,n_] :=
(* generates a list of the n smallest k-almost-primes *)
Module[{firstnprimes, runningkprimes = {}},
firstnprimes = Prime[Range[n]];
runningkprimes = firstnprimes;
Do[
runningkprimes =
Outer[Times, firstnprimes , runningkprimes ] // Flatten // Union  // Take[#, n] & ;
(* only keep lowest n numbers in our running list *)
, {i, 1, k - 1}];
runningkprimes
]
(* now to create table with n=10 and k ranging from 1 to 5 *)
Table[Flatten[{"k = " <> ToString[i] <> ": ", kprimes[i, 10]}], {i,1,5}] // TableForm
```

{{out}}

```k = 1: 	2	3	5	7	11	13	17	19	23	29
k = 2: 	4	6	9	10	14	15	21	22	25	26
k = 3: 	8	12	18	20	27	28	30	42	44	45
k = 4: 	16	24	36	40	54	56	60	81	84	88
k = 5: 	32	48	72	80	108	112	120	162	168	176
```

```MODULE AlmostPrime;
FROM FormatString IMPORT FormatString;

PROCEDURE KPrime(n,k : INTEGER) : BOOLEAN;
VAR p,f : INTEGER;
BEGIN
f := 0;
p := 2;
WHILE (f<k) AND (p*p<=n) DO
WHILE n MOD p = 0 DO
n := n DIV p;
INC(f)
END;
INC(p)
END;
IF n>1 THEN
RETURN f+1 = k
END;
RETURN f = k
END KPrime;

VAR
buf : ARRAY[0..63] OF CHAR;
i,c,k : INTEGER;
BEGIN
FOR k:=1 TO 5 DO
FormatString("k = %i:", buf, k);
WriteString(buf);

i:=2;
c:=0;
WHILE c<10 DO
IF KPrime(i,k) THEN
FormatString(" %i", buf, i);
WriteString(buf);
INC(c)
END;
INC(i)
END;

WriteLn;
END;

END AlmostPrime.
```

## Nim

```proc prime(k: int, listLen: int): seq[int] =
result = @[]
var
test: int = 2
curseur: int = 0
while curseur < listLen:
var
i: int = 2
compte = 0
n = test
while i <= n:
if (n mod i)==0:
n = n div i
compte += 1
else:
i += 1
if compte == k:
curseur += 1
test += 1

for k in 1..5:
echo "k = ",k," : ",prime(k,10)
```

{{out}}

```k = 1 : @[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
k = 2 : @[4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
k = 3 : @[8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
k = 4 : @[16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
k = 5 : @[32, 48, 72, 80, 108, 112, 120, 162, 168, 176]
```

## Objeck

{{trans|C}}

```class Kth_Prime {
function : native : kPrime(n : Int, k : Int) ~ Bool {
f := 0;
for (p := 2; f < k & p*p <= n; p+=1;) {
while (0 = n % p) {
n /= p; f+=1;
};
};

return f + ((n > 1) ? 1 : 0) = k;
}

function : Main(args : String[]) ~ Nil {
for (k := 1; k <= 5; k+=1;) {
"k = {\$k}:"->Print();

c := 0;
for (i := 2; c < 10; i+=1;) {
if (kPrime(i, k)) {
" {\$i}"->Print();
c+=1;
};
};
'\n'->Print();
};
}
}
```

{{out}}

```
k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176
```

## Oforth

```: kprime?( n k -- b )
| i |
0 2 n for: i [
while( n i /mod swap 0 = ) [ ->n 1+ ] drop
]
k ==
;

: table( k -- [] )
| l |
Array new dup ->l
2 while (l size 10 <>) [ dup k kprime? if dup l add then 1+ ]
drop
;
```

{{out}}

```
>#[ table .cr ] 5 each
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
[4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
[8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
[16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
[32, 48, 72, 80, 108, 112, 120, 162, 168, 176]

```

## PARI/GP

```almost(k)=my(n); for(i=1,10,while(bigomega(n++)!=k,); print1(n", "));
for(k=1,5,almost(k);print)
```

{{out}}

```2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
4, 6, 9, 10, 14, 15, 21, 22, 25, 26,
8, 12, 18, 20, 27, 28, 30, 42, 44, 45,
16, 24, 36, 40, 54, 56, 60, 81, 84, 88,
32, 48, 72, 80, 108, 112, 120, 162, 168, 176,
```

## Pascal

```program AlmostPrime;
{\$IFDEF FPC}
{\$Mode Delphi}
{\$ENDIF}
uses
primtrial;
var
i,K,cnt : longWord;
BEGIN
K := 1;
repeat
cnt := 0;
i := 2;
write('K=',K:2,':');
repeat
if isAlmostPrime(i,K) then
Begin
write(i:6,' ');
inc(cnt);
end;
inc(i);
until cnt = 9;
writeln;
inc(k);
until k > 10;
END.
```

;output:

```K= 1 :    2     3     5     7    11    13    17    19    23    29
K= 2 :    4     6     9    10    14    15    21    22    25    26
K= 3 :    8    12    18    20    27    28    30    42    44    45
K= 4 :   16    24    36    40    54    56    60    81    84    88
K= 5 :   32    48    72    80   108   112   120   162   168   176
K= 6 :   64    96   144   160   216   224   240   324   336   352
K= 7 :  128   192   288   320   432   448   480   648   672   704
K= 8 :  256   384   576   640   864   896   960  1296  1344  1408
K= 9 :  512   768  1152  1280  1728  1792  1920  2592  2688  2816
K=10 : 1024  1536  2304  2560  3456  3584  3840  5184  5376  5632
```

## Perl

Using a CPAN module, which is simple and fast: {{libheader|ntheory}}

```use ntheory qw/factor/;
sub almost {
my(\$k,\$n) = @_;
my \$i = 1;
map { \$i++ while scalar factor(\$i) != \$k; \$i++ } 1..\$n;
}
say "\$_ : ", join(" ", almost(\$_,10)) for 1..5;
```

{{out}}

```
1 : 2 3 5 7 11 13 17 19 23 29
2 : 4 6 9 10 14 15 21 22 25 26
3 : 8 12 18 20 27 28 30 42 44 45
4 : 16 24 36 40 54 56 60 81 84 88
5 : 32 48 72 80 108 112 120 162 168 176

```

or writing everything by hand:

```use strict;
use warnings;

sub k_almost_prime;

for my \$k ( 1 .. 5 ) {
my \$almost = 0;
print join(", ", map {
1 until k_almost_prime ++\$almost, \$k;
"\$almost";
} 1 .. 10), "\n";
}

sub nth_prime;

sub k_almost_prime {
my (\$n, \$k) = @_;
return if \$n <= 1 or \$k < 1;
my \$which_prime = 0;
for my \$count ( 1 .. \$k ) {
while( \$n % nth_prime \$which_prime ) {
++\$which_prime;
}
\$n /= nth_prime \$which_prime;
return if \$n == 1 and \$count != \$k;
}
(\$n == 1) ? 1 : ();
}

BEGIN {
# This is loosely based on one of the python solutions
# to the RC Sieve of Eratosthenes task.
my @primes = (2, 3, 5, 7);
my \$p_iter = 1;
my \$p = \$primes[\$p_iter];
my \$q = \$p*\$p;
my %sieve;
my \$candidate = \$primes[-1] + 2;
sub nth_prime {
my \$n = shift;
return if \$n < 0;
OUTER: while( \$#primes < \$n ) {
while( my \$s = delete \$sieve{\$candidate} ) {
my \$next = \$s + \$candidate;
\$next += \$s while exists \$sieve{\$next};
\$sieve{\$next} = \$s;
\$candidate += 2;
}
while( \$candidate < \$q ) {
push @primes, \$candidate;
\$candidate += 2;
next OUTER if exists \$sieve{\$candidate};
}
my \$twop = 2 * \$p;
my \$next = \$q + \$twop;
\$next += \$twop while exists \$sieve{\$next};
\$sieve{\$next} = \$twop;
\$p = \$primes[++\$p_iter];
\$q = \$p * \$p;
\$candidate += 2;
}
return \$primes[\$n];
}
}
```

{{out}}

```2, 3, 5, 7, 11, 13, 17, 19, 23, 29
4, 6, 9, 10, 14, 15, 21, 22, 25, 26
8, 12, 18, 20, 27, 28, 30, 42, 44, 45
16, 24, 36, 40, 54, 56, 60, 81, 84, 88
32, 48, 72, 80, 108, 112, 120, 162, 168, 176

```

## Perl 6

{{trans|C}} {{works with|Rakudo|2015.12}}

```sub is-k-almost-prime(\$n is copy, \$k) returns Bool {
loop (my (\$p, \$f) = 2, 0; \$f < \$k && \$p*\$p <= \$n; \$p++) {
\$n /= \$p, \$f++ while \$n %% \$p;
}
\$f + (\$n > 1) == \$k;
}

for 1 .. 5 -> \$k {
say ~.[^10]
given grep { is-k-almost-prime(\$_, \$k) }, 2 .. *
}
```

{{out}}

```2 3 5 7 11 13 17 19 23 29
4 6 9 10 14 15 21 22 25 26
8 12 18 20 27 28 30 42 44 45
16 24 36 40 54 56 60 81 84 88
32 48 72 80 108 112 120 162 168 176
```

Here is a solution with identical output based on the factors routine from [[Count_in_factors#Perl_6]] (to be included manually until we decide where in the distribution to put it).

```constant @primes = 2, |(3, 5, 7 ... *).grep: *.is-prime;

multi sub factors(1) { 1 }
multi sub factors(Int \$remainder is copy) {
gather for @primes -> \$factor {
# if remainder < factor², we're done
if \$factor * \$factor > \$remainder {
take \$remainder if \$remainder > 1;
last;
}
# How many times can we divide by this prime?
while \$remainder %% \$factor {
take \$factor;
last if (\$remainder div= \$factor) === 1;
}
}
}

constant @factory = lazy 0..* Z=> flat (0, 0, map { +factors(\$_) }, 2..*);

sub almost(\$n) { map *.key, grep *.value == \$n, @factory }

put almost(\$_)[^10] for 1..5;
```

## Phix

```
-- Naieve stuff, mostly, but coded with enthuiasm!
-- Following the idea behind (but not the code from!) the J submission:
--  Generate 10 primes (kept in p10)                            -- (print K=1)
--  Multiply each of them by the first ten primes
--  Sort and find unique values, take the first ten of those    -- (print K=2)
--  Multiply each of them by the first ten primes
--  Sort and find unique values, take the first ten of those    -- (print K=3)
--  ...
-- However I just keep a "top 10", using a bubble insertion, and stop
--  multiplying as soon as everything else for p10[i] will be too big.

-- (as calculated earlier from this routine,
--  or that "return 1" in pi() works just fine.)
--constant f17={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59}
constant f17={2,3,5,7,11,13,17}

function pi(integer n)
-- approximates the number of primes less than or equal to n
--  if n<=10 then return 4 end if
--  -- best estimate
--  return floor(n/(log(n)-1))
--  if n<=20 then return 1 end if -- (or use a table:)
if n<17 then
for i=1 to length(f17) do
if n<=f17[i] then return i end if
end for
end if
--  -- upper bound for n>=17 (Rosser and Schoenfeld 1962):
--  return floor(1.25506*n/log(n))
-- lower bound for n>=17 (Rosser and Schoenfeld 1962):
return floor(n/log(n))
end function

function primes(integer n)
-- return the first n prime numbers (tested 0 to 20,000, which took ~86s)
sequence prime
integer count = 0
integer lowN, highN, midN

-- First, iteratively estimate the sieve size required
lowN = 2*n
highN = n*n+1
while lowN<highN do
midN = floor((lowN+highN)/2)
if pi(midN)>n then
highN = midN
else
lowN = midN+1
end if
end while
-- Then apply standard sieve and store primes as we find
-- them towards the (no longer used) start of the sieve.
prime = repeat(1,highN)
for i=2 to highN do
if prime[i] then
count += 1
prime[count] = i
if count>=n then exit end if
for k=i+i to highN by i do
prime[k] = 0
end for
end if
end for
return prime[1..n]
end function

procedure display(integer k, sequence kprimes)
printf(1,"%d: ",k)
for i=1 to length(kprimes) do
printf(1,"%5d",kprimes[i])
end for
puts(1,"\n")
end procedure

function bubble(sequence next, integer v)
-- insert v into next (discarding next[\$]), keeping next in ascending order
-- (relies on next[1] /always/ being smaller that anything that we insert.)
for i=length(next)-1 to 1 by -1 do
if v>next[i] then
next[i+1] = v
exit
end if
next[i+1] = next[i]
end for
return next
end function

procedure almost_prime()
sequence p10 = primes(10)
sequence apk = p10  -- (almostprime[k])
sequence next = repeat(0,length(p10))
integer high, test
for k=1 to 5 do
display(k,apk)
if k=5 then exit end if
next = apk
for i=1 to length(p10) do
--          next[i] = apk[i]*p10[1]
next[i] = apk[i]*2
end for
high = next[\$]
for i=2 to length(p10) do
for j=1 to length(next) do
test = apk[j]*p10[i]
if not find(test,next) then
if test>high then exit end if
next = bubble(next,test)
high = next[\$]
end if
end for
end for
apk = next
end for
if getc(0) then end if
end procedure

almost_prime()

```

{{out}}

```
1:     2    3    5    7   11   13   17   19   23   29
2:     4    6    9   10   14   15   21   22   25   26
3:     8   12   18   20   27   28   30   42   44   45
4:    16   24   36   40   54   56   60   81   84   88
5:    32   48   72   80  108  112  120  162  168  176

```

and a translation of the C version, with improved variable names and some extra notes

```

function kprime(integer n, integer k)
--
-- returns true if n has exactly k factors
--
-- p is a "pseudo prime" in that 2,3,4,5,6,7,8,9,10,11 will behave
--  exactly like 2,3,5,7,11, ie the remainder(n,4)=0 (etc) will never
--  succeed because remainder(n,2) would have succeeded twice first.
--  Hence for larger n consider replacing p+=1 with p=next_prime(),
--  then again, on "" this performs an obscene number of divisions..
--
integer p = 2,
factors = 0

while factors<k and p*p<=n do
while remainder(n,p)=0 do
n = n/p
factors += 1
end while
p += 1
end while
factors += (n>1)
return factors==k
end function

procedure almost_primeC()
integer nextkprime, count

for k=1 to 5 do
printf(1,"k = %d: ", k);
nextkprime = 2
count = 0
while count<10 do
if kprime(nextkprime, k) then
printf(1," %4d", nextkprime)
count += 1
end if
nextkprime += 1
end while
puts(1,"\n")
end for
if getc(0) then end if
end procedure

almost_primeC()

```

{{out}}

```
k = 1:     2    3    5    7   11   13   17   19   23   29
k = 2:     4    6    9   10   14   15   21   22   25   26
k = 3:     8   12   18   20   27   28   30   42   44   45
k = 4:    16   24   36   40   54   56   60   81   84   88
k = 5:    32   48   72   80  108  112  120  162  168  176

```

## PicoLisp

```(de factor (N)
(make
(let
(D 2
L (1 2 2 . (4 2 4 2 4 6 2 6 .))
M (sqrt N) )
(while (>= M D)
(if (=0 (% N D))
(setq M
(sqrt (setq N (/ N (link D)))) )
(inc 'D (pop 'L)) ) )

(de almost (N)
(let (X 2  Y 0)
(make
(loop
(when (and (nth (factor X) N) (not (cdr @)))
(inc 'Y) )
(T (= 10 Y) 'done)
(inc 'X) ) ) ) )

(for I 5
(println I '-> (almost I) ) )

(bye)
```

## Potion

```# Converted from C
kprime = (n, k):
p = 2, f = 0
while (f < k && p*p <= n):
while (0 == n % p):
n /= p
f++.
p++.
n = if (n > 1): 1.
else: 0.
f + n == k.

1 to 5 (k):
"k = " print, k print, ":" print
i = 2, c = 0
while (c < 10):
if (kprime(i, k)): " " print, i print, c++.
i++
.
"" say.
```

C and Potion take 0.006s, Perl5 0.028s

## Prolog

```% almostPrime(K, +Take, List) succeeds if List can be unified with the
% first Take K-almost-primes.
% Notice that K need not be specified.
% To avoid having to cache or recompute the first Take primes, we define
% almostPrime/3 in terms of almostPrime/4 as follows:
%
almostPrime(K, Take, List) :-
% Compute the list of the first Take primes:
nPrimes(Take, Primes),
almostPrime(K, Take, Primes, List).

almostPrime(1, Take, Primes, Primes).

almostPrime(K, Take, Primes, List) :-
generate(2, K),  % generate K >= 2
K1 is K - 1,
almostPrime(K1, Take, Primes, L),
multiplylist( Primes, L, Long),
sort(Long, Sorted), % uniquifies
take(Take, Sorted, List).

```

That's it. The rest is machinery. For portability, a compatibility section is included below.

```nPrimes( M, Primes) :- nPrimes( [2], M, Primes).

nPrimes( Accumulator, I, Primes) :-
next_prime(Accumulator, Prime),
append(Accumulator, [Prime], Next),
length(Next, N),
( N = I -> Primes = Next; nPrimes( Next, I, Primes)).

% next_prime(+Primes, NextPrime) succeeds if NextPrime is the next
% prime after a list, Primes, of consecutive primes starting at 2.
next_prime([2], 3).
next_prime([2|Primes], P) :-
last(Primes, PP),
P2 is PP + 2,
generate(P2, N),
1 is N mod 2,		        % odd
Max is floor(sqrt(N+1)),	% round-off paranoia
forall( (member(Prime, [2|Primes]),
(Prime =< Max -> true
; (!, fail))), N mod Prime > 0 ),
!,
P = N.

% multiply( +A, +List, Answer )
multiply( A, [], [] ).
multiply( A, [X|Xs], [AX|As] ) :-
AX is A * X,
multiply(A, Xs, As).

% multiplylist( L1, L2, List ) succeeds if List is the concatenation of X * L2
% for successive elements X of L1.
multiplylist( [], B, [] ).
multiplylist( [A|As], B, List ) :-
multiply(A, B, L1),
multiplylist(As, B, L2),
append(L1, L2, List).

```
```%%%%% compatibility section %%%%%

:- if(current_prolog_flag(dialect, yap)).
generate(Min, I) :- between(Min, inf, I).

append([],L,L).
append([X|Xs], L, [X|Ls]) :- append(Xs,L,Ls).

:- endif.

:- if(current_prolog_flag(dialect, swi)).
generate(Min, I) :- between(Min, inf, I).
:- endif.

:- if(current_prolog_flag(dialect, yap)).
append([],L,L).
append([X|Xs], L, [X|Ls]) :- append(Xs,L,Ls).

last([X], X).
last([_|Xs],X) :- last(Xs,X).

:- endif.

:- if(current_prolog_flag(dialect, gprolog)).
generate(Min, I) :-
current_prolog_flag(max_integer, Max),
between(Min, Max, I).
:- endif.

```

Example using SWI-Prolog:

```
?- between(1,5,I),
(almostPrime(I, 10, L) -> writeln(L)), fail.

[2,3,5,7,11,13,17,19,23,29]
[4,6,9,10,14,15,21,22,25,26]
[8,12,18,20,27,28,30,42,44,45]
[16,24,36,40,54,56,60,81,84,88]
[32,48,72,80,108,112,120,162,168,176]

?- time( (almostPrime(5, 10, L), writeln(L))).
[32,48,72,80,108,112,120,162,168,176]
% 1,906 inferences, 0.001 CPU in 0.001 seconds (84% CPU, 2388471 Lips)

```

## PureBasic

{{trans|C}}

```EnableExplicit

Procedure.b kprime(n.i, k.i)
Define p.i = 2,
f.i = 0

While f < k And p*p <= n
While n % p = 0
n / p
f + 1
Wend
p + 1
Wend

ProcedureReturn Bool(f + Bool(n > 1) = k)

EndProcedure

;___main____
If Not OpenConsole("Almost prime")
End -1
EndIf

Define i.i,
c.i,
k.i

For k = 1 To 5
Print("k = " + Str(k) + ":")

i = 2
c = 0
While c < 10
If kprime(i, k)
Print(RSet(Str(i),4))
c + 1
EndIf
i + 1
Wend
PrintN("")
Next

Input()
```

{{out}}

```k = 1:   2   3   5   7  11  13  17  19  23  29
k = 2:   4   6   9  10  14  15  21  22  25  26
k = 3:   8  12  18  20  27  28  30  42  44  45
k = 4:  16  24  36  40  54  56  60  81  84  88
k = 5:  32  48  72  80 108 112 120 162 168 176
```

## Python

This imports [[Prime decomposition#Python]]

```from prime_decomposition import decompose
from itertools import islice, count
try:
from functools import reduce
except:
pass

def almostprime(n, k=2):
d = decompose(n)
try:
terms = [next(d) for i in range(k)]
return reduce(int.__mul__, terms, 1) == n
except:
return False

if __name__ == '__main__':
for k in range(1,6):
print('%i: %r' % (k, list(islice((n for n in count() if almostprime(n, k)), 10))))
```

{{out}}

```1: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
2: [4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
3: [8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
4: [16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
5: [32, 48, 72, 80, 108, 112, 120, 162, 168, 176]
```

### An updated version with no import dependencies.

```
# k-Almost-primes
# Python 3.6.3
# no imports

def prime_factors(m=2):

for i in range(2, m):
r, q = divmod(m, i)
if not q:
return [i] + prime_factors(r)
return [m]

def k_almost_primes(n, k=2):
multiples = set()
lists = list()
for x in range(k+1):
lists.append([])

for i in range(2, n+1):
if i not in multiples:
if len(lists[1]) < 10:
lists[1].append(i)
multiples.update(range(i*i, n+1, i))
print("k=1: {}".format(lists[1]))

for j in range(2, k+1):
for m in multiples:
l = prime_factors(m)
ll = len(l)
if ll == j and len(lists[j]) < 10:
lists[j].append(m)

print("k={}: {}".format(j, lists[j]))

k_almost_primes(200, 5)
# try:
#k_almost_primes(6000, 10)

```

{{out}}

```
>>> %Run k_almost_primes.py
k=1: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
k=2: [4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
k=3: [8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
k=4: [16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
k=5: [32, 48, 72, 80, 108, 112, 120, 162, 168, 176]

```

## R

This uses the function from [[Prime decomposition#R]]

```#
### =========================================================

# Find k-Almost-primes
# R implementation
#
### =========================================================

#---------------------------------------------------------------
# Function for prime factorization from Rosetta Code
#---------------------------------------------------------------

findfactors <- function(n) {
d <- c()
div <- 2; nxt <- 3; rest <- n
while( rest != 1 ) {
while( rest%%div == 0 ) {
d <- c(d, div)
rest <- floor(rest / div)
}
div <- nxt
nxt <- nxt + 2
}
d
}

#---------------------------------------------------------------
# Find k-Almost-primes
#---------------------------------------------------------------

almost_primes <- function(n = 10, k = 5) {

# Set up matrix for storing of the results

res <- matrix(NA, nrow = k, ncol = n)
rownames(res) <- paste("k = ", 1:k, sep = "")
colnames(res) <- rep("", n)

# Loop over k

for (i in 1:k) {

tmp <- 1

while (any(is.na(res[i, ]))) { # Keep looping if there are still missing entries in the result-matrix
if (length(findfactors(tmp)) == i) { # Check number of factors
res[i, which.max(is.na(res[i, ]))] <- tmp
}
tmp <- tmp + 1
}
}
print(res)
}
```

{{out}}

```
k = 1  2  3  5  7  11  13  17  19  23  29
k = 2  4  6  9 10  14  15  21  22  25  26
k = 3  8 12 18 20  27  28  30  42  44  45
k = 4 16 24 36 40  54  56  60  81  84  88
k = 5 32 48 72 80 108 112 120 162 168 176

```

## Racket

```#lang racket
(require (only-in math/number-theory factorize))

(define ((k-almost-prime? k) n)
(= k (for/sum ((f (factorize n))) (cadr f))))

(define KAP-table-values
(for/list ((k (in-range 1 (add1 5))))
(define kap? (k-almost-prime? k))
(for/list ((j (in-range 10)) (i (sequence-filter kap? (in-naturals 1))))
i)))

(define (format-table t)
(define longest-number-length
(add1 (order-of-magnitude (argmax order-of-magnitude (cons (length t) (apply append t))))))
(define (fmt-val v) (~a v #:width longest-number-length #:align 'right))
(string-join
(for/list ((r t) (k (in-naturals 1)))
(string-append
(format "║ k = ~a║ " (fmt-val k))
(string-join (for/list ((c r)) (fmt-val c)) "| ")
"║"))
"\n"))

(displayln (format-table KAP-table-values))
```

{{out}}

```║ k =   1║   2|   3|   5|   7|  11|  13|  17|  19|  23|  29║
║ k =   2║   4|   6|   9|  10|  14|  15|  21|  22|  25|  26║
║ k =   3║   8|  12|  18|  20|  27|  28|  30|  42|  44|  45║
║ k =   4║  16|  24|  36|  40|  54|  56|  60|  81|  84|  88║
║ k =   5║  32|  48|  72|  80| 108| 112| 120| 162| 168| 176║
```

## REXX

### naive version

The method used is to count the number of factors in the number to determine the K-primality.

The first three '''k-almost''' primes for each '''K''' group are computed directly (rather than found).

```/*REXX program  computes and displays  the  first  N  K─almost  primes  from   1 ──► K. */
parse arg N K .                                  /*get optional arguments from the C.L. */
if N=='' | N==","  then N=10                     /*N  not specified?   Then use default.*/
if K=='' | K==","  then K= 5                     /*K   "      "          "   "     "    */
/*W: is the width of K, used for output*/
do m=1  for  K;     \$=2**m;  fir=\$           /*generate & assign 1st K─almost prime.*/
#=1;                if #==N  then leave      /*#: K─almost primes; Enough are found?*/
#=2;                \$=\$  3*(2**(m-1))        /*generate & append 2nd K─almost prime.*/
if #==N  then leave                          /*#: K─almost primes; Enough are found?*/
if m==1  then _=fir + fir                    /* [↓]  gen & append 3rd K─almost prime*/
else do;  _=9 * (2**(m-2));    #=3;    \$=\$  _;    end
do j=_ + m - 1   until #==N              /*process an  K─almost prime  N  times.*/
if factr()\==m  then iterate             /*not the correct  K─almost  prime?    */
#=# + 1;         \$=\$ j                   /*bump K─almost counter; append it to \$*/
end   /*j*/                              /* [↑]   generate  N  K─almost  primes.*/
say right(m, length(K))"─almost ("N') primes:'     \$
end       /*m*/                              /* [↑]  display a line for each K─prime*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
factr: z=j;                    do f=0  while z// 2==0;  z=z% 2;  end  /*divisible by  2.*/
do f=f  while z// 3==0;  z=z% 3;  end  /*divisible  "  3.*/
do f=f  while z// 5==0;  z=z% 5;  end  /*divisible  "  5.*/
do f=f  while z// 7==0;  z=z% 7;  end  /*divisible  "  7.*/
do f=f  while z//11==0;  z=z%11;  end  /*divisible  " 11.*/
do f=f  while z//13==0;  z=z%13;  end  /*divisible  " 13.*/
do p=17  by 6  while  p<=z              /*insure  P  isn't divisible by three. */
parse var  p   ''  -1  _                /*obtain the right─most decimal digit. */
/* [↓]  fast check for divisible by 5. */
if _\==5  then do; do f=f+1  while z//p==0; z=z%p; end;  f=f-1; end  /*÷ by P? */
if _ ==3  then iterate                  /*fast check for  X  divisible by five.*/
x=p+2;             do f=f+1  while z//x==0; z=z%x; end;  f=f-1       /*÷ by X? */
end   /*i*/                             /* [↑]  find all the factors in  Z.    */

if f==0  then return 1                    /*if  prime (f==0),  then return unity.*/
```

{{out|output|text= when using the default input:}}

```
1─almost (10) primes: 2 3 5 7 11 13 17 19 23 29
2─almost (10) primes: 4 6 9 10 14 15 21 22 25 26
3─almost (10) primes: 8 12 18 20 27 28 30 42 44 45
4─almost (10) primes: 16 24 36 40 54 56 60 81 84 88
5─almost (10) primes: 32 48 72 80 108 112 120 162 168 176

```

{{out|output|text= when using the input of: 20 12 }}

```
1─almost (20) primes: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
2─almost (20) primes: 4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57
3─almost (20) primes: 8 12 18 20 27 28 30 42 44 45 50 52 63 66 68 70 75 76 78 92
4─almost (20) primes: 16 24 36 40 54 56 60 81 84 88 90 100 104 126 132 135 136 140 150 152
5─almost (20) primes: 32 48 72 80 108 112 120 162 168 176 180 200 208 243 252 264 270 272 280 300
6─almost (20) primes: 64 96 144 160 216 224 240 324 336 352 360 400 416 486 504 528 540 544 560 600
7─almost (20) primes: 128 192 288 320 432 448 480 648 672 704 720 800 832 972 1008 1056 1080 1088 1120 1200
8─almost (20) primes: 256 384 576 640 864 896 960 1296 1344 1408 1440 1600 1664 1944 2016 2112 2160 2176 2240 2400
9─almost (20) primes: 512 768 1152 1280 1728 1792 1920 2592 2688 2816 2880 3200 3328 3888 4032 4224 4320 4352 4480 4800
10─almost (20) primes: 1024 1536 2304 2560 3456 3584 3840 5184 5376 5632 5760 6400 6656 7776 8064 8448 8640 8704 8960 9600
11─almost (20) primes: 2048 3072 4608 5120 6912 7168 7680 10368 10752 11264 11520 12800 13312 15552 16128 16896 17280 17408 17920 19200
12─almost (20) primes: 4096 6144 9216 10240 13824 14336 15360 20736 21504 22528 23040 25600 26624 31104 32256 33792 34560 34816 35840 38400

```

### optimized version

This optimized REXX version can be ''over a hundred times'' faster than the naive version.

Some of the optimizations are: :::* calculating the first 2(K-1) K─almost primes for each '''K''' group :::* generating the primes (up to the limit) instead of dividing by (most) divisors. :::* extending the ''up-front'' prime divisors in the '''factr''' function.

The 1st optimization (bullet) allows the direct computation (instead of searching) of all K─almost primes up to the first ''odd'' prime in the list.

Once the required primes are generated, the finding of the K─almost primes is almost instantaneous.

```/*REXX program  computes and displays  the first    N    K─almost primes from  1 ──► K. */
parse arg N K .                                  /*obtain optional arguments from the CL*/
if N=='' | N==','  then N=10                     /*N  not specified?   Then use default.*/
if K=='' | K==','  then K= 5                     /*K   "      "          "   "     "    */
nn=N;  N=abs(N);   w=length(K)                   /*N positive? Then show K─almost primes*/
limit= (2**K) * N / 2                            /*this is the limit for most K-primes. */
if N==1  then limit=limit * 2                    /*  "   "  "    "    "  a    N    of 1.*/
if K==1  then limit=limit * 4                    /*  "   "  "    "    "  a K─prime  " 2.*/
if K==2  then limit=limit * 2                    /*  "   "  "    "    "  "    "     " 4.*/
if K==3  then limit=limit * 3 % 2                /*  "   "  "    "    "  "    "     " 8.*/
call genPrimes  limit + 1                        /*generate primes up to the  LIMIT + 1.*/
say 'The highest prime computed: '        @.#        " (under the limit of " limit').'
say                                              /* [↓]  define where 1st K─prime is odd*/
d.=0;  d.2=  2;  d.3 =  4;  d.4 =  7;  d.5 = 13;  d.6 = 22;  d.7 =  38;   d.8=63
d.9=102;  d.10=168;  d.11=268;  d.12=426;  d.13=673;  d.14=1064
d!=0
do m=1  for  K;    d!=max(d!,d.m)            /*generate & assign 1st K─almost prime.*/
mr=right(m,w);     mm=m-1

\$=;           do #=1  to min(N, d!)          /*assign some doubled K─almost primes. */
\$=\$  d.mm.# * 2
end   /*#*/
#=#-1
if m==1  then from=2
else from=1 + word(\$, words(\$) )

do j=from   until  #==N                  /*process an  K─almost prime  N  times.*/
if factr()\==m  then iterate             /*not the correct  K─almost  prime?    */
#=#+1;   \$=\$ j                           /*bump K─almost counter; append it to \$*/
end   /*j*/                              /* [↑]   generate  N  K─almost  primes.*/

if nn>0  then say mr"─almost ("N') primes:'     \$
else say '    the last'  mr  "K─almost prime: "   word(\$, words(\$))
/* [↓]  assign K─almost primes.*/
do q=1  for #;     d.m.q=word(\$,q)             ;   end  /*q*/
do q=1  for #;  if d.m.q\==d.mm.q*2  then leave;   end  /*q*/
/* [↑]  count doubly-duplicates*/
/*──── say copies('─',40)  'for '   m", "   q-1   'numbers were doubly─duplicated.' ────*/
/*──── say                                                                          ────*/
end       /*m*/                              /* [↑]  display a line for each K─prime*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
factr: if #.j\==.  then return #.j
z=j;                                do f=0 while z// 2==0; z=z% 2; end   /*÷ by 2*/
do f=f while z// 3==0; z=z% 3; end   /*÷ "  3*/
do f=f while z// 5==0; z=z% 5; end   /*÷ "  5*/
do f=f while z// 7==0; z=z% 7; end   /*÷ "  7*/
do f=f while z//11==0; z=z%11; end   /*÷ " 11*/
do f=f while z//13==0; z=z%13; end   /*÷ " 13*/
do f=f while z//17==0; z=z%17; end   /*÷ " 17*/
do f=f while z//19==0; z=z%19; end   /*÷ " 19*/

do i=9    while  @.i<=z;       d=@.i    /*divide by some higher primes.        */
do f=f  while z//d==0;   z=z%d;  end  /*is  Z  divisible by the  prime  D ?  */
end   /*i*/                             /* [↑]  find all factors in  Z.        */

if f==0  then f=1;   #.j=f;   return f    /*Is prime (f≡0)?   Then return unity. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
genPrimes: arg x;             @.=;      @.1=2;     @.2=3;    #.=.;     #=2;     s.#=@.#**2
do j=@.# +2  by 2  to x             /*only find odd primes from here on.   */
do p=2  while s.p<=j             /*divide by some known low odd primes. */
if j//@.p==0  then iterate j     /*Is  J  divisible by X?  Then ¬ prime.*/
end   /*p*/                      /* [↓]  a prime  (J)  has been found.  */
#=#+1;    @.#=j;   #.j=1;   s.#=j*j /*bump prime count, and also assign ···*/
end      /*j*/                      /* ··· the # of factors, prime, prime².*/
return                                /* [↑]  not an optimal prime generator.*/
```

{{out|output|text= when using the input of: 20 16 }}

```
The highest prime computed:  655357  (under the limit of  655360).

1─almost (20) primes:  2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
2─almost (20) primes:  4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57
3─almost (20) primes:  8 12 18 20 27 28 30 42 44 45 50 52 63 66 68 70 75 76 78 92
4─almost (20) primes:  16 24 36 40 54 56 60 81 84 88 90 100 104 126 132 135 136 140 150 152
5─almost (20) primes:  32 48 72 80 108 112 120 162 168 176 180 200 208 243 252 264 270 272 280 300
6─almost (20) primes:  64 96 144 160 216 224 240 324 336 352 360 400 416 486 504 528 540 544 560 600
7─almost (20) primes:  128 192 288 320 432 448 480 648 672 704 720 800 832 972 1008 1056 1080 1088 1120 1200
8─almost (20) primes:  256 384 576 640 864 896 960 1296 1344 1408 1440 1600 1664 1944 2016 2112 2160 2176 2240 2400
9─almost (20) primes:  512 768 1152 1280 1728 1792 1920 2592 2688 2816 2880 3200 3328 3888 4032 4224 4320 4352 4480 4800
10─almost (20) primes:  1024 1536 2304 2560 3456 3584 3840 5184 5376 5632 5760 6400 6656 7776 8064 8448 8640 8704 8960 9600
11─almost (20) primes:  2048 3072 4608 5120 6912 7168 7680 10368 10752 11264 11520 12800 13312 15552 16128 16896 17280 17408 17920 19200
12─almost (20) primes:  4096 6144 9216 10240 13824 14336 15360 20736 21504 22528 23040 25600 26624 31104 32256 33792 34560 34816 35840 38400
13─almost (20) primes:  8192 12288 18432 20480 27648 28672 30720 41472 43008 45056 46080 51200 53248 62208 64512 67584 69120 69632 71680 76800
14─almost (20) primes:  16384 24576 36864 40960 55296 57344 61440 82944 86016 90112 92160 102400 106496 124416 129024 135168 138240 139264 143360 153600
15─almost (20) primes:  32768 49152 73728 81920 110592 114688 122880 165888 172032 180224 184320 204800 212992 248832 258048 270336 276480 278528 286720 307200
16─almost (20) primes:  65536 98304 147456 163840 221184 229376 245760 331776 344064 360448 368640 409600 425984 497664 516096 540672 552960 557056 573440 614400

```

## Ring

```
for ap = 1 to 5
see "k = " + ap + ":"
aList = []
for n = 1 to 200
num = 0
for nr = 1 to n
if n%nr=0 and isPrime(nr)=1
num = num + 1
pr = nr
while true
pr = pr * nr
if n%pr = 0
num = num + 1
else exit ok
end ok
next
if (ap = 1 and isPrime(n) = 1) or (ap > 1 and num = ap)
if len(aList)=10 exit ok ok
next
for m = 1 to len(aList)
see " " + aList[m]
next
see nl
next

func isPrime num
if (num <= 1) return 0 ok
if (num % 2 = 0 and num != 2) return 0 ok
for i = 3 to floor(num / 2) -1 step 2
if (num % i = 0) return 0 ok
next
return 1

```

Output:

```
k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176

```

## Ruby

```require 'prime'

def almost_primes(k=2)
1.step {|n| yield n if n.prime_division.sum( &:last ) == k }
end

(1..5).each{|k| puts almost_primes(k).take(10).join(", ")}
```

{{out}}

```
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
4, 6, 9, 10, 14, 15, 21, 22, 25, 26
8, 12, 18, 20, 27, 28, 30, 42, 44, 45
16, 24, 36, 40, 54, 56, 60, 81, 84, 88
32, 48, 72, 80, 108, 112, 120, 162, 168, 176

```

{{trans|J}}

```require 'prime'

p ar = pr = Prime.take(10)
4.times{p ar = ar.product(pr).map{|(a,b)| a*b}.uniq.sort.take(10)}
```

{{out}}

```
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
[4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
[8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
[16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
[32, 48, 72, 80, 108, 112, 120, 162, 168, 176]

```

## Rust

```fn is_kprime(n: u32, k: u32) -> bool {
let mut primes = 0;
let mut f = 2;
let mut rem = n;
while primes < k && rem > 1{
while (rem % f) == 0 && rem > 1{
rem /= f;
primes += 1;
}
f += 1;
}
rem == 1 && primes == k
}

struct KPrimeGen {
k: u32,
n: u32,
}

impl Iterator for KPrimeGen {
type Item = u32;
fn next(&mut self) -> Option<u32> {
self.n += 1;
while !is_kprime(self.n, self.k) {
self.n += 1;
}
Some(self.n)
}
}

fn kprime_generator(k: u32) -> KPrimeGen {
KPrimeGen {k: k, n: 1}
}

fn main() {
for k in 1..6 {
println!("{}: {:?}", k, kprime_generator(k).take(10).collect::<Vec<_>>());
}
}
```

{{out}}

```
1: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
2: [4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
3: [8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
4: [16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
5: [32, 48, 72, 80, 108, 112, 120, 162, 168, 176]

```

## Scala

```def isKPrime(n: Int, k: Int, d: Int = 2): Boolean = (n, k, d) match {
case (n, k, _) if n == 1 => k == 0
case (n, _, d) if n % d == 0 => isKPrime(n / d, k - 1, d)
case (_, _, _) => isKPrime(n, k, d + 1)
}

def kPrimeStream(k: Int): Stream[Int] = {
def loop(n: Int): Stream[Int] =
if (isKPrime(n, k)) n #:: loop(n+ 1)
else loop(n + 1)
loop(2)
}

for (k <- 1 to 5) {
println( s"\$k: [\${ kPrimeStream(k).take(10) mkString " " }]" )
}
```

{{out}}

```
1: [2 3 5 7 11 13 17 19 23 29]
2: [4 6 9 10 14 15 21 22 25 26]
3: [8 12 18 20 27 28 30 42 44 45]
4: [16 24 36 40 54 56 60 81 84 88]
5: [32 48 72 80 108 112 120 162 168 176]

```

## SequenceL

```;
import <Utilities/Sequence.sl>;

main(args(2)) :=
let
result := firstNKPrimes(1 ... 5, 10);

output[i] := "k = " ++ intToString(i) ++ ": " ++ delimit(intToString(result[i]), ' ');
in
delimit(output, '\n');

firstNKPrimes(k, N) := firstNKPrimesHelper(k, N, 2, []);

firstNKPrimesHelper(k, N, current, result(1)) :=
let
newResult := result when not isKPrime(k, current) else result ++ [current];
in
result when size(result) = N
else
firstNKPrimesHelper(k, N, current + 1, newResult);

isKPrime(k, n) := size(primeFactorization(n)) = k;
```

Using Prime Decomposition Solution [http://rosettacode.org/wiki/Prime_decomposition#SequenceL]

{{out}}

```
main.exe
"k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176"

```

## Seed7

```\$ include "seed7_05.s7i";

const func boolean: kprime (in var integer: number, in integer: k) is func
result
var boolean: kprime is FALSE;
local
var integer: p is 2;
var integer: f is 0;
begin
while f < k and p * p <= number do
while number rem p = 0 do
number := number div p;
incr(f);
end while;
incr(p);
end while;
kprime := f + ord(number > 1) = k;
end func;

const proc: main is func
local
var integer: k is 0;
var integer: number is 0;
var integer: count is 0;
begin
for k range 1 to 5 do
write("k = " <& k <& ":");
count := 0;
for number range 2 to integer.last until count >= 10 do
if kprime(number, k) then
write(" " <& number);
incr(count);
end if;
end for;
writeln;
end for;
end func;
```

{{out}}

```
k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176

```

## Sidef

{{trans|Perl 6}}

```func is_k_almost_prime(n, k) {
for (var (p, f) = (2, 0); (f < k) && (p*p <= n); ++p) {
(n /= p; ++f) while (p `divides` n)
}
n > 1 ? (f.inc == k) : (f == k)
}

{ |k|
var x = 10
say gather {
{ |i|
if (is_k_almost_prime(i, k)) {
take(i)
--x == 0 && break
}
} << 1..Inf
}
} << 1..5
```

{{out}}

```
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
[4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
[8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
[16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
[32, 48, 72, 80, 108, 112, 120, 162, 168, 176]

```

## Tcl

{{works with|Tcl|8.6}} {{tcllib|math::numtheory}}

```package require Tcl 8.6
package require math::numtheory

proc firstNprimes n {
for {set result {};set i 2} {[llength \$result] < \$n} {incr i} {
if {[::math::numtheory::isprime \$i]} {
lappend result \$i
}
}
return \$result
}

proc firstN_KalmostPrimes {n k} {
set p [firstNprimes \$n]
set i [lrepeat \$k 0]
set c {}

while true {
dict set c [::tcl::mathop::* {*}[lmap j \$i {lindex \$p \$j}]] ""
for {set x 0} {\$x < \$k} {incr x} {
lset i \$x [set xx [expr {([lindex \$i \$x] + 1) % \$n}]]
if {\$xx} break
}
if {\$x == \$k} break
}
return [lrange [lsort -integer [dict keys \$c]] 0 [expr {\$n - 1}]]
}

for {set K 1} {\$K <= 5} {incr K} {
puts "\$K => [firstN_KalmostPrimes 10 \$K]"
}
```

{{out}}

```
1 => 2 3 5 7 11 13 17 19 23 29
2 => 4 6 9 10 14 15 21 22 25 26
3 => 8 12 18 20 27 28 30 42 44 45
4 => 16 24 36 40 54 56 60 81 84 88
5 => 32 48 72 80 108 112 120 162 168 176

```

## uBasic/4tH

{{trans|C}} Local(3)

For c@ = 1 To 5 Print "k = ";c@;": ";

b@=0

For a@ = 2 Step 1 While b@ < 10 If FUNC(_kprime (a@,c@)) Then b@ = b@ + 1 Print " ";a@; EndIf Next

Print Next

End

_kprime Param(2) Local(2)

d@ = 0 For c@ = 2 Step 1 While (d@ < b@) * ((c@ * c@) < (a@ + 1)) Do While (a@ % c@) = 0 a@ = a@ / c@ d@ = d@ + 1 Loop Next Return (b@ = (d@ + (a@ > 1)))

```
{{out}}

```txt
k = 1:  2 3 5 7 11 13 17 19 23 29
k = 2:  4 6 9 10 14 15 21 22 25 26
k = 3:  8 12 18 20 27 28 30 42 44 45
k = 4:  16 24 36 40 54 56 60 81 84 88
k = 5:  32 48 72 80 108 112 120 162 168 176

0 OK, 0:200
```

## VBA

{{trans|Phix}}

```Private Function kprime(ByVal n As Integer, k As Integer) As Boolean
Dim p As Integer, factors As Integer
p = 2
factors = 0
Do While factors < k And p * p <= n
Do While n Mod p = 0
n = n / p
factors = factors + 1
Loop
p = p + 1
Loop
factors = factors - (n > 1) 'true=-1
kprime = factors = k
End Function

Private Sub almost_primeC()
Dim nextkprime As Integer, count As Integer
Dim k As Integer
For k = 1 To 5
Debug.Print "k ="; k; ":";
nextkprime = 2
count = 0
Do While count < 10
If kprime(nextkprime, k) Then
Debug.Print " "; Format(CStr(nextkprime), "@@@@@");
count = count + 1
End If
nextkprime = nextkprime + 1
Loop
Debug.Print
Next k
End Sub
```

{{out}}

```k = 1 :     2     3     5     7    11    13    17    19    23    29
k = 2 :     4     6     9    10    14    15    21    22    25    26
k = 3 :     8    12    18    20    27    28    30    42    44    45
k = 4 :    16    24    36    40    54    56    60    81    84    88
k = 5 :    32    48    72    80   108   112   120   162   168   176
```

## VBScript

Repurposed the VBScript code for the Prime Decomposition task.

```
For k = 1 To 5
count = 0
increment = 1
WScript.StdOut.Write "K" & k & ": "
Do Until count = 10
If PrimeFactors(increment) = k Then
WScript.StdOut.Write increment & " "
count = count + 1
End If
increment = increment + 1
Loop
WScript.StdOut.WriteLine
Next

Function PrimeFactors(n)
PrimeFactors = 0
arrP = Split(ListPrimes(n)," ")
divnum = n
Do Until divnum = 1
For i = 0 To UBound(arrP)-1
If divnum = 1 Then
Exit For
ElseIf divnum Mod arrP(i) = 0 Then
divnum = divnum/arrP(i)
PrimeFactors = PrimeFactors + 1
End If
Next
Loop
End Function

Function IsPrime(n)
If n = 2 Then
IsPrime = True
ElseIf n <= 1 Or n Mod 2 = 0 Then
IsPrime = False
Else
IsPrime = True
For i = 3 To Int(Sqr(n)) Step 2
If n Mod i = 0 Then
IsPrime = False
Exit For
End If
Next
End If
End Function

Function ListPrimes(n)
ListPrimes = ""
For i = 1 To n
If IsPrime(i) Then
ListPrimes = ListPrimes & i & " "
End If
Next
End Function

```

{{Out}}

```
K1: 2 3 5 7 11 13 17 19 23 29
K2: 4 6 9 10 14 15 21 22 25 26
K3: 8 12 18 20 27 28 30 42 44 45
K4: 16 24 36 40 54 56 60 81 84 88
K5: 32 48 72 80 108 112 120 162 168 176

```

## Visual Basic .NET

{{trans|C#}}

```Module Module1

Class KPrime
Public K As Integer

Public Function IsKPrime(number As Integer) As Boolean
Dim primes = 0
Dim p = 2
While p * p <= number AndAlso primes < K
While number Mod p = 0 AndAlso primes < K
number = number / p
primes = primes + 1
End While
p = p + 1
End While
If number > 1 Then
primes = primes + 1
End If
Return primes = K
End Function

Public Function GetFirstN(n As Integer) As List(Of Integer)
Dim result As New List(Of Integer)
Dim number = 2
While result.Count < n
If IsKPrime(number) Then
End If
number = number + 1
End While
Return result
End Function
End Class

Sub Main()
For Each k In Enumerable.Range(1, 5)
Dim kprime = New KPrime With {
.K = k
}
Console.WriteLine("k = {0}: {1}", k, String.Join(" ", kprime.GetFirstN(10)))
Next
End Sub

End Module
```

{{out}}

```k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176
```

## XBasic

{{trans|FreeBASIC}} {{works with|Windows XBasic}}

```
PROGRAM "almostprime"
VERSION "0.0001"

DECLARE FUNCTION Entry()
INTERNAL FUNCTION KPrime(n%%, k%%)

FUNCTION Entry()
FOR k@@ = 1 TO 5
PRINT "k ="; k@@; ": ";
i%% = 2
c%% = 0
DO WHILE c%% < 10
IFT KPrime(i%%, k@@) THEN
PRINT FORMAT\$("### ", i%%);
INC c%%
END IF
INC i%%
LOOP
PRINT
NEXT k@@
END FUNCTION

FUNCTION KPrime(n%%, k%%)
f%% = 0
FOR i%% = 2 TO n%%
DO WHILE n%% MOD i%% = 0
IF f%% = k%% THEN RETURN \$\$FALSE
INC f%%
n%% = n%% \ i%%
LOOP
NEXT i%%
RETURN f%% = k%%
END FUNCTION

END PROGRAM

```

{{out}}

```
k = 1:   2   3   5   7  11  13  17  19  23  29
k = 2:   4   6   9  10  14  15  21  22  25  26
k = 3:   8  12  18  20  27  28  30  42  44  45
k = 4:  16  24  36  40  54  56  60  81  84  88
k = 5:  32  48  72  80 108 112 120 162 168 176

```

## Yabasic

{{trans|Lua}}

```// Returns boolean indicating whether n is k-almost prime
sub almostPrime(n, k)
local divisor, count

divisor = 2

while(count < (k + 1) and n <> 1)
if not mod(n, divisor) then
n = n / divisor
count = count + 1
else
divisor = divisor + 1
end if
wend
return count = k
end sub

// Generates table containing first ten k-almost primes for given k
sub kList(k, kTab())
local n, i

n = 2^k : i = 1
while(i < 11)
if almostPrime(n, k) then
kTab(i) = n
i = i + 1
end if
n = n + 1
wend
end sub

// Main procedure, displays results from five calls to kList()
dim kTab(10)
for k = 1 to 5
print "k = ", k, " : ";
kList(k, kTab())
for n = 1 to 10
print kTab(n), ", ";
next
print "..."
next
```

## zkl

{{trans|Ruby}}{{trans|J}} Using the prime generator from task [[Extensible prime generator#zkl]].

Can't say I entirely understand this algorithm. Uses list comprehension to calculate the outer/tensor product (p10 ⊗ ar).

```primes:=Utils.Generator(Import("sieve").postponed_sieve);
(p10:=ar:=primes.walk(10)).println();
do(4){
(ar=([[(x,y);ar;p10;'*]] : Utils.Helpers.listUnique(_).sort()[0,10])).println();
}
```

{{out}}

```
L(2,3,5,7,11,13,17,19,23,29)
L(4,6,9,10,14,15,21,22,25,26)
L(8,12,18,20,27,28,30,42,44,45)
L(16,24,36,40,54,56,60,81,84,88)
L(32,48,72,80,108,112,120,162,168,176)

```

## ZX Spectrum Basic

{{trans|AWK}}

```10 FOR k=1 TO 5
20 PRINT k;":";
30 LET c=0: LET i=1
40 IF c=10 THEN GO TO 100
50 LET i=i+1
60 GO SUB 1000
70 IF r THEN PRINT " ";i;: LET c=c+1
90 GO TO 40
100 PRINT
110 NEXT k
120 STOP
1000 REM kprime
1010 LET p=2: LET n=i: LET f=0
1020 IF f=k OR (p*p)>n THEN GO TO 1100
1030 IF n/p=INT (n/p) THEN LET n=n/p: LET f=f+1: GO TO 1030
1040 LET p=p+1: GO TO 1020
1100 LET r=(f+(n>1)=k)
1110 RETURN
```

{{out}}

```1: 2 3 5 7 11 13 17 19 23 29
2: 4 6 9 10 14 15 21 22 25 26
3: 8 12 18 20 27 28 30 42 44 45
4: 16 24 36 40 54 56 60 81 84 88
5: 32 48 72 80 108 112 120 162 168 176
```