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{{task}}
A number is an ''attractive number'' if the number of its prime factors (whether distinct or not) is also prime.
;Example: The number '''20''', whose prime decomposition is '''2 × 2 × 5''', is an ''attractive number'' because the number of its prime factors ('''3''') is also prime.
;Task: Show sequence items up to '''120'''.
;Reference: :* The OEIS entry: [http://oeis.org/A063989 A063989 attractive numbers].
AWK
# syntax: GAWK -f ATTRACTIVE_NUMBERS.AWK
# converted from C
BEGIN {
limit = 120
printf("attractive numbers from 1-%d:\n",limit)
for (i=1; i<=limit; i++) {
n = count_prime_factors(i)
if (is_prime(n)) {
printf("%d ",i)
}
}
printf("\n")
exit(0)
}
function count_prime_factors(n, count,f) {
f = 2
if (n == 1) { return(0) }
if (is_prime(n)) { return(1) }
while (1) {
if (!(n % f)) {
count++
n /= f
if (n == 1) { return(count) }
if (is_prime(n)) { f = n }
}
else if (f >= 3) { f += 2 }
else { f = 3 }
}
}
function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
}
{{out}}
attractive numbers from 1-120:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34 35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68 69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99 102 105 106 108 110 111 112 114 115 116 117 118 119 120
C
{{trans|Go}}
#include <stdio.h>
#define TRUE 1
#define FALSE 0
#define MAX 120
typedef int bool;
bool is_prime(int n) {
int d = 5;
if (n < 2) return FALSE;
if (!(n % 2)) return n == 2;
if (!(n % 3)) return n == 3;
while (d *d <= n) {
if (!(n % d)) return FALSE;
d += 2;
if (!(n % d)) return FALSE;
d += 4;
}
return TRUE;
}
int count_prime_factors(int n) {
int count = 0, f = 2;
if (n == 1) return 0;
if (is_prime(n)) return 1;
while (TRUE) {
if (!(n % f)) {
count++;
n /= f;
if (n == 1) return count;
if (is_prime(n)) f = n;
}
else if (f >= 3) f += 2;
else f = 3;
}
}
int main() {
int i, n, count = 0;
printf("The attractive numbers up to and including %d are:\n", MAX);
for (i = 1; i <= MAX; ++i) {
n = count_prime_factors(i);
if (is_prime(n)) {
printf("%4d", i);
if (!(++count % 20)) printf("\n");
}
}
printf("\n");
return 0;
}
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
C++
{{trans|C}}
#include <iostream>
#include <iomanip>
#define MAX 120
using namespace std;
bool is_prime(int n) {
if (n < 2) return false;
if (!(n % 2)) return n == 2;
if (!(n % 3)) return n == 3;
int d = 5;
while (d *d <= n) {
if (!(n % d)) return false;
d += 2;
if (!(n % d)) return false;
d += 4;
}
return true;
}
int count_prime_factors(int n) {
if (n == 1) return 0;
if (is_prime(n)) return 1;
int count = 0, f = 2;
while (true) {
if (!(n % f)) {
count++;
n /= f;
if (n == 1) return count;
if (is_prime(n)) f = n;
}
else if (f >= 3) f += 2;
else f = 3;
}
}
int main() {
cout << "The attractive numbers up to and including " << MAX << " are:" << endl;
for (int i = 1, count = 0; i <= MAX; ++i) {
int n = count_prime_factors(i);
if (is_prime(n)) {
cout << setw(4) << i;
if (!(++count % 20)) cout << endl;
}
}
cout << endl;
return 0;
}
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
C#
{{trans|D}}
using System;
namespace AttractiveNumbers {
class Program {
const int MAX = 120;
static bool IsPrime(int n) {
if (n < 2) return false;
if (n % 2 == 0) return n == 2;
if (n % 3 == 0) return n == 3;
int d = 5;
while (d * d <= n) {
if (n % d == 0) return false;
d += 2;
if (n % d == 0) return false;
d += 4;
}
return true;
}
static int PrimeFactorCount(int n) {
if (n == 1) return 0;
if (IsPrime(n)) return 1;
int count = 0;
int f = 2;
while (true) {
if (n % f == 0) {
count++;
n /= f;
if (n == 1) return count;
if (IsPrime(n)) f = n;
} else if (f >= 3) {
f += 2;
} else {
f = 3;
}
}
}
static void Main(string[] args) {
Console.WriteLine("The attractive numbers up to and including {0} are:", MAX);
int i = 1;
int count = 0;
while (i <= MAX) {
int n = PrimeFactorCount(i);
if (IsPrime(n)) {
Console.Write("{0,4}", i);
if (++count % 20 == 0) Console.WriteLine();
}
++i;
}
Console.WriteLine();
}
}
}
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
D
{{trans|C++}}
import std.stdio;
enum MAX = 120;
bool isPrime(int n) {
if (n < 2) return false;
if (n % 2 == 0) return n == 2;
if (n % 3 == 0) return n == 3;
int d = 5;
while (d * d <= n) {
if (n % d == 0) return false;
d += 2;
if (n % d == 0) return false;
d += 4;
}
return true;
}
int primeFactorCount(int n) {
if (n == 1) return 0;
if (isPrime(n)) return 1;
int count;
int f = 2;
while (true) {
if (n % f == 0) {
count++;
n /= f;
if (n == 1) return count;
if (isPrime(n)) f = n;
} else if (f >= 3) {
f += 2;
} else {
f = 3;
}
}
}
void main() {
writeln("The attractive numbers up to and including ", MAX, " are:");
int i = 1;
int count;
while (i <= MAX) {
int n = primeFactorCount(i);
if (isPrime(n)) {
writef("%4d", i);
if (++count % 20 == 0) writeln;
}
++i;
}
writeln;
}
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
Factor
{{works with|Factor|0.99}}
USING: formatting grouping io math.primes math.primes.factors
math.ranges sequences ;
"The attractive numbers up to and including 120 are:" print
120 [1,b] [ factors length prime? ] filter 20 <groups>
[ [ "%4d" printf ] each nl ] each
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
FreeBASIC
{{trans|D}}
Const limite = 120
Declare Function esPrimo(n As Integer) As Boolean
Declare Function ContandoFactoresPrimos(n As Integer) As Integer
Function esPrimo(n As Integer) As Boolean
If n < 2 Then Return false
If n Mod 2 = 0 Then Return n = 2
If n Mod 3 = 0 Then Return n = 3
Dim As Integer d = 5
While d * d <= n
If n Mod d = 0 Then Return false
d += 2
If n Mod d = 0 Then Return false
d += 4
Wend
Return true
End Function
Function ContandoFactoresPrimos(n As Integer) As Integer
If n = 1 Then Return false
If esPrimo(n) Then Return true
Dim As Integer f = 2, contar = 0
While true
If n Mod f = 0 Then
contar += 1
n = n / f
If n = 1 Then Return contar
If esPrimo(n) Then f = n
Elseif f >= 3 Then
f += 2
Else
f = 3
End If
Wend
End Function
' Mostrar la sucencia de números atractivos hasta 120.
Dim As Integer i = 1, longlinea = 0
Print "Los numeros atractivos hasta e incluyendo"; limite; " son: "
While i <= limite
Dim As Integer n = ContandoFactoresPrimos(i)
If esPrimo(n) Then
Print Using "####"; i;
longlinea += 1: If longlinea Mod 20 = 0 Then Print ""
End If
i += 1
Wend
End
{{out}}
Los numeros atractivos hasta e incluyendo 120 son:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
Go
Simple functions to test for primality and to count prime factors suffice here.
package main
import "fmt"
func isPrime(n int) bool {
switch {
case n < 2:
return false
case n%2 == 0:
return n == 2
case n%3 == 0:
return n == 3
default:
d := 5
for d*d <= n {
if n%d == 0 {
return false
}
d += 2
if n%d == 0 {
return false
}
d += 4
}
return true
}
}
func countPrimeFactors(n int) int {
switch {
case n == 1:
return 0
case isPrime(n):
return 1
default:
count, f := 0, 2
for {
if n%f == 0 {
count++
n /= f
if n == 1 {
return count
}
if isPrime(n) {
f = n
}
} else if f >= 3 {
f += 2
} else {
f = 3
}
}
return count
}
}
func main() {
const max = 120
fmt.Println("The attractive numbers up to and including", max, "are:")
count := 0
for i := 1; i <= max; i++ {
n := countPrimeFactors(i)
if isPrime(n) {
fmt.Printf("%4d", i)
count++
if count % 20 == 0 {
fmt.Println()
}
}
}
fmt.Println()
}
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
Groovy
{{trans|Java}}
class AttractiveNumbers {
static boolean isPrime(int n) {
if (n < 2) return false
if (n % 2 == 0) return n == 2
if (n % 3 == 0) return n == 3
int d = 5
while (d * d <= n) {
if (n % d == 0) return false
d += 2
if (n % d == 0) return false
d += 4
}
return true
}
static int countPrimeFactors(int n) {
if (n == 1) return 0
if (isPrime(n)) return 1
int count = 0, f = 2
while (true) {
if (n % f == 0) {
count++
n /= f
if (n == 1) return count
if (isPrime(n)) f = n
} else if (f >= 3) f += 2
else f = 3
}
}
static void main(String[] args) {
final int max = 120
printf("The attractive numbers up to and including %d are:\n", max)
int count = 0
for (int i = 1; i <= max; ++i) {
int n = countPrimeFactors(i)
if (isPrime(n)) {
printf("%4d", i)
if (++count % 20 == 0) println()
}
}
println()
}
}
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
Haskell
import Data.Numbers.Primes
import Data.Bool (bool)
attractiveNumbers :: [Integer]
attractiveNumbers =
[1 ..] >>= (bool [] . return) <*> (isPrime . length . primeFactors)
main :: IO ()
main = print $ takeWhile (<= 120) attractiveNumbers
Or equivalently, as a list comprehension:
import Data.Numbers.Primes
attractiveNumbers :: [Integer]
attractiveNumbers =
[ x
| x <- [1 ..]
, isPrime (length (primeFactors x)) ]
main :: IO ()
main = print $ takeWhile (<= 120) attractiveNumbers
Or simply:
import Data.Numbers.Primes
attractiveNumbers :: [Integer]
attractiveNumbers =
filter
(isPrime . length . primeFactors)
[1 ..]
main :: IO ()
main = print $ takeWhile (<= 120) attractiveNumbers
{{Out}}
[4,6,8,9,10,12,14,15,18,20,21,22,25,26,27,28,30,32,33,34,35,38,39,42,44,45,46,48,49,50,51,52,55,57,58,62,63,65,66,68,69,70,72,74,75,76,77,78,80,82,85,86,87,91,92,93,94,95,98,99,102,105,106,108,110,111,112,114,115,116,117,118,119,120]
Java
{{trans|C}}
public class Attractive {
static boolean is_prime(int n) {
if (n < 2) return false;
if (n % 2 == 0) return n == 2;
if (n % 3 == 0) return n == 3;
int d = 5;
while (d *d <= n) {
if (n % d == 0) return false;
d += 2;
if (n % d == 0) return false;
d += 4;
}
return true;
}
static int count_prime_factors(int n) {
if (n == 1) return 0;
if (is_prime(n)) return 1;
int count = 0, f = 2;
while (true) {
if (n % f == 0) {
count++;
n /= f;
if (n == 1) return count;
if (is_prime(n)) f = n;
}
else if (f >= 3) f += 2;
else f = 3;
}
}
public static void main(String[] args) {
final int max = 120;
System.out.printf("The attractive numbers up to and including %d are:\n", max);
for (int i = 1, count = 0; i <= max; ++i) {
int n = count_prime_factors(i);
if (is_prime(n)) {
System.out.printf("%4d", i);
if (++count % 20 == 0) System.out.println();
}
}
System.out.println();
}
}
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
Julia
using Primes
# oneliner is println("The attractive numbers from 1 to 120 are:\n", filter(x -> isprime(sum(values(factor(x)))), 1:120))
isattractive(n) = isprime(sum(values(factor(n))))
printattractive(m, n) = println("The attractive numbers from $m to $n are:\n", filter(isattractive, m:n))
printattractive(1, 120)
{{out}}
The attractive numbers from 1 to 120 are:
[4, 6, 8, 9, 10, 12, 14, 15, 18, 20, 21, 22, 25, 26, 27, 28, 30, 32, 33, 34, 35, 38, 39, 42, 44, 45, 46, 48, 49, 50, 51, 52, 55, 57, 58, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 102, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120]
Kotlin
{{trans|Go}}
// Version 1.3.21
const val MAX = 120
fun isPrime(n: Int) : Boolean {
if (n < 2) return false
if (n % 2 == 0) return n == 2
if (n % 3 == 0) return n == 3
var d : Int = 5
while (d * d <= n) {
if (n % d == 0) return false
d += 2
if (n % d == 0) return false
d += 4
}
return true
}
fun countPrimeFactors(n: Int) =
when {
n == 1 -> 0
isPrime(n) -> 1
else -> {
var nn = n
var count = 0
var f = 2
while (true) {
if (nn % f == 0) {
count++
nn /= f
if (nn == 1) break
if (isPrime(nn)) f = nn
} else if (f >= 3) {
f += 2
} else {
f = 3
}
}
count
}
}
fun main() {
println("The attractive numbers up to and including $MAX are:")
var count = 0
for (i in 1..MAX) {
val n = countPrimeFactors(i)
if (isPrime(n)) {
System.out.printf("%4d", i)
if (++count % 20 == 0) println()
}
}
println()
}
{{output}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
LLVM
; This is not strictly LLVM, as it uses the C library function "printf".
; LLVM does not provide a way to print values, so the alternative would be
; to just load the string into memory, and that would be boring.
$"ATTRACTIVE_STR" = comdat any
$"FORMAT_NUMBER" = comdat any
$"NEWLINE_STR" = comdat any
@"ATTRACTIVE_STR" = linkonce_odr unnamed_addr constant [52 x i8] c"The attractive numbers up to and including %d are:\0A\00", comdat, align 1
@"FORMAT_NUMBER" = linkonce_odr unnamed_addr constant [4 x i8] c"%4d\00", comdat, align 1
@"NEWLINE_STR" = linkonce_odr unnamed_addr constant [2 x i8] c"\0A\00", comdat, align 1
;--- The declaration for the external C printf function.
declare i32 @printf(i8*, ...)
; Function Attrs: noinline nounwind optnone uwtable
define zeroext i1 @is_prime(i32) #0 {
%2 = alloca i1, align 1 ;-- allocate return value
%3 = alloca i32, align 4 ;-- allocate n
%4 = alloca i32, align 4 ;-- allocate d
store i32 %0, i32* %3, align 4 ;-- store local copy of n
store i32 5, i32* %4, align 4 ;-- store 5 in d
%5 = load i32, i32* %3, align 4 ;-- load n
%6 = icmp slt i32 %5, 2 ;-- n < 2
br i1 %6, label %nlt2, label %niseven
nlt2:
store i1 false, i1* %2, align 1 ;-- store false in return value
br label %exit
niseven:
%7 = load i32, i32* %3, align 4 ;-- load n
%8 = srem i32 %7, 2 ;-- n % 2
%9 = icmp ne i32 %8, 0 ;-- (n % 2) != 0
br i1 %9, label %odd, label %even
even:
%10 = load i32, i32* %3, align 4 ;-- load n
%11 = icmp eq i32 %10, 2 ;-- n == 2
store i1 %11, i1* %2, align 1 ;-- store (n == 2) in return value
br label %exit
odd:
%12 = load i32, i32* %3, align 4 ;-- load n
%13 = srem i32 %12, 3 ;-- n % 3
%14 = icmp ne i32 %13, 0 ;-- (n % 3) != 0
br i1 %14, label %loop, label %div3
div3:
%15 = load i32, i32* %3, align 4 ;-- load n
%16 = icmp eq i32 %15, 3 ;-- n == 3
store i1 %16, i1* %2, align 1 ;-- store (n == 3) in return value
br label %exit
loop:
%17 = load i32, i32* %4, align 4 ;-- load d
%18 = load i32, i32* %4, align 4 ;-- load d
%19 = mul nsw i32 %17, %18 ;-- d * d
%20 = load i32, i32* %3, align 4 ;-- load n
%21 = icmp sle i32 %19, %20 ;-- (d * d) <= n
br i1 %21, label %first, label %prime
first:
%22 = load i32, i32* %3, align 4 ;-- load n
%23 = load i32, i32* %4, align 4 ;-- load d
%24 = srem i32 %22, %23 ;-- n % d
%25 = icmp ne i32 %24, 0 ;-- (n % d) != 0
br i1 %25, label %second, label %notprime
second:
%26 = load i32, i32* %4, align 4 ;-- load d
%27 = add nsw i32 %26, 2 ;-- increment d by 2
store i32 %27, i32* %4, align 4 ;-- store d
%28 = load i32, i32* %3, align 4 ;-- load n
%29 = load i32, i32* %4, align 4 ;-- load d
%30 = srem i32 %28, %29 ;-- n % d
%31 = icmp ne i32 %30, 0 ;-- (n % d) != 0
br i1 %31, label %loop_end, label %notprime
loop_end:
%32 = load i32, i32* %4, align 4 ;-- load d
%33 = add nsw i32 %32, 4 ;-- increment d by 4
store i32 %33, i32* %4, align 4 ;-- store d
br label %loop
notprime:
store i1 false, i1* %2, align 1 ;-- store false in return value
br label %exit
prime:
store i1 true, i1* %2, align 1 ;-- store true in return value
br label %exit
exit:
%34 = load i1, i1* %2, align 1 ;-- load return value
ret i1 %34
}
; Function Attrs: noinline nounwind optnone uwtable
define i32 @count_prime_factors(i32) #0 {
%2 = alloca i32, align 4 ;-- allocate return value
%3 = alloca i32, align 4 ;-- allocate n
%4 = alloca i32, align 4 ;-- allocate count
%5 = alloca i32, align 4 ;-- allocate f
store i32 %0, i32* %3, align 4 ;-- store local copy of n
store i32 0, i32* %4, align 4 ;-- store zero in count
store i32 2, i32* %5, align 4 ;-- store 2 in f
%6 = load i32, i32* %3, align 4 ;-- load n
%7 = icmp eq i32 %6, 1 ;-- n == 1
br i1 %7, label %eq1, label %ne1
eq1:
store i32 0, i32* %2, align 4 ;-- store zero in return value
br label %exit
ne1:
%8 = load i32, i32* %3, align 4 ;-- load n
%9 = call zeroext i1 @is_prime(i32 %8) ;-- is n prime?
br i1 %9, label %prime, label %loop
prime:
store i32 1, i32* %2, align 4 ;-- store a in return value
br label %exit
loop:
%10 = load i32, i32* %3, align 4 ;-- load n
%11 = load i32, i32* %5, align 4 ;-- load f
%12 = srem i32 %10, %11 ;-- n % f
%13 = icmp ne i32 %12, 0 ;-- (n % f) != 0
br i1 %13, label %br2, label %br1
br1:
%14 = load i32, i32* %4, align 4 ;-- load count
%15 = add nsw i32 %14, 1 ;-- increment count
store i32 %15, i32* %4, align 4 ;-- store count
%16 = load i32, i32* %5, align 4 ;-- load f
%17 = load i32, i32* %3, align 4 ;-- load n
%18 = sdiv i32 %17, %16 ;-- n / f
store i32 %18, i32* %3, align 4 ;-- n = n / f
%19 = load i32, i32* %3, align 4 ;-- load n
%20 = icmp eq i32 %19, 1 ;-- n == 1
br i1 %20, label %br1_1, label %br1_2
br1_1:
%21 = load i32, i32* %4, align 4 ;-- load count
store i32 %21, i32* %2, align 4 ;-- store the count in the return value
br label %exit
br1_2:
%22 = load i32, i32* %3, align 4 ;-- load n
%23 = call zeroext i1 @is_prime(i32 %22) ;-- is n prime?
br i1 %23, label %br1_3, label %loop
br1_3:
%24 = load i32, i32* %3, align 4 ;-- load n
store i32 %24, i32* %5, align 4 ;-- f = n
br label %loop
br2:
%25 = load i32, i32* %5, align 4 ;-- load f
%26 = icmp sge i32 %25, 3 ;-- f >= 3
br i1 %26, label %br2_1, label %br3
br2_1:
%27 = load i32, i32* %5, align 4 ;-- load f
%28 = add nsw i32 %27, 2 ;-- increment f by 2
store i32 %28, i32* %5, align 4 ;-- store f
br label %loop
br3:
store i32 3, i32* %5, align 4 ;-- store 3 in f
br label %loop
exit:
%29 = load i32, i32* %2, align 4 ;-- load return value
ret i32 %29
}
; Function Attrs: noinline nounwind optnone uwtable
define i32 @main() #0 {
%1 = alloca i32, align 4 ;-- allocate i
%2 = alloca i32, align 4 ;-- allocate n
%3 = alloca i32, align 4 ;-- count
store i32 0, i32* %3, align 4 ;-- store zero in count
%4 = call i32 (i8*, ...) @printf(i8* getelementptr inbounds ([52 x i8], [52 x i8]* @"ATTRACTIVE_STR", i32 0, i32 0), i32 120)
store i32 1, i32* %1, align 4 ;-- store 1 in i
br label %loop
loop:
%5 = load i32, i32* %1, align 4 ;-- load i
%6 = icmp sle i32 %5, 120 ;-- i <= 120
br i1 %6, label %loop_body, label %exit
loop_body:
%7 = load i32, i32* %1, align 4 ;-- load i
%8 = call i32 @count_prime_factors(i32 %7) ;-- count factors of i
store i32 %8, i32* %2, align 4 ;-- store factors in n
%9 = call zeroext i1 @is_prime(i32 %8) ;-- is n prime?
br i1 %9, label %prime_branch, label %loop_inc
prime_branch:
%10 = load i32, i32* %1, align 4 ;-- load i
%11 = call i32 (i8*, ...) @printf(i8* getelementptr inbounds ([4 x i8], [4 x i8]* @"FORMAT_NUMBER", i32 0, i32 0), i32 %10)
%12 = load i32, i32* %3, align 4 ;-- load count
%13 = add nsw i32 %12, 1 ;-- increment count
store i32 %13, i32* %3, align 4 ;-- store count
%14 = srem i32 %13, 20 ;-- count % 20
%15 = icmp ne i32 %14, 0 ;-- (count % 20) != 0
br i1 %15, label %loop_inc, label %row_end
row_end:
%16 = call i32 (i8*, ...) @printf(i8* getelementptr inbounds ([2 x i8], [2 x i8]* @"NEWLINE_STR", i32 0, i32 0))
br label %loop_inc
loop_inc:
%17 = load i32, i32* %1, align 4 ;-- load i
%18 = add nsw i32 %17, 1 ;-- increment i
store i32 %18, i32* %1, align 4 ;-- store i
br label %loop
exit:
%19 = call i32 (i8*, ...) @printf(i8* getelementptr inbounds ([2 x i8], [2 x i8]* @"NEWLINE_STR", i32 0, i32 0))
ret i32 0
}
attributes #0 = { noinline nounwind optnone uwtable "correctly-rounded-divide-sqrt-fp-math"="false" "disable-tail-calls"="false" "less-precise-fpmad"="false" "no-frame-pointer-elim"="false" "no-infs-fp-math"="false" "no-jump-tables"="false" "no-nans-fp-math"="false" "no-signed-zeros-fp-math"="false" "no-trapping-math"="false" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+fxsr,+mmx,+sse,+sse2,+x87" "unsafe-fp-math"="false" "use-soft-float"="false" }
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
Lua
-- Returns true if x is prime, and false otherwise
function isPrime (x)
if x < 2 then return false end
if x < 4 then return true end
if x % 2 == 0 then return false end
for d = 3, math.sqrt(x), 2 do
if x % d == 0 then return false end
end
return true
end
-- Compute the prime factors of n
function factors (n)
local facList, divisor, count = {}, 1
if n < 2 then return facList end
while not isPrime(n) do
while not isPrime(divisor) do divisor = divisor + 1 end
count = 0
while n % divisor == 0 do
n = n / divisor
table.insert(facList, divisor)
end
divisor = divisor + 1
if n == 1 then return facList end
end
table.insert(facList, n)
return facList
end
-- Main procedure
for i = 1, 120 do
if isPrime(#factors(i)) then io.write(i .. "\t") end
end
{{out}}
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27
28 30 32 33 34 35 38 39 42 44 45 46 48 49 50
51 52 55 57 58 62 63 65 66 68 69 70 72 74 75
76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
Maple
attractivenumbers := proc(n::posint)
local an, i;
an :=[]:
for i from 1 to n do
if isprime(NumberTheory:-NumberOfPrimeFactors(i)) then
an := [op(an), i]:
end if:
end do:
end proc:
attractivenumbers(120);
{{out}}
[4, 6, 8, 9, 10, 12, 14, 15, 18, 20, 21, 22, 25, 26, 27, 28, 30, 32, 33, 34, 35, 38, 39, 42, 44, 45, 46, 48, 49, 50, 51, 52, 55, 57, 58, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 102, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120]
Nim
{{trans|C}}
import strformat
const MAX = 120
proc isPrime(n: int): bool =
var d = 5
if n < 2:
return false
if n mod 2 == 0:
return n == 2
if n mod 3 == 0:
return n == 3
while d * d <= n:
if n mod d == 0:
return false
inc d, 2
if n mod d == 0:
return false
inc d, 4
return true
proc countPrimeFactors(n_in: int): int =
var count = 0
var f = 2
var n = n_in
if n == 1:
return 0
if isPrime(n):
return 1
while true:
if n mod f == 0:
inc count
n = n div f
if n == 1:
return count
if isPrime(n):
f = n
elif (f >= 3):
inc f, 2
else:
f = 3
proc main() =
var n, count: int = 0
echo fmt"The attractive numbers up to and including {MAX} are:"
for i in 1..MAX:
n = countPrimeFactors(i)
if isPrime(n):
write(stdout, fmt"{i:4d}")
inc count
if count mod 20 == 0:
write(stdout, "\n")
write(stdout, "\n")
main()
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
Perl
{{libheader|ntheory}}
use ntheory <is_prime factor>;
is_prime +factor $_ and print "$_ " for 1..120;
{{out}}
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34 35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68 69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99 102 105 106 108 110 111 112 114 115 116 117 118 119 120
Perl 6
{{works with|Rakudo|2019.03}} This algorithm is concise but not really well suited to finding large quantities of consecutive attractive numbers. It works, but isn't especially speedy. More than a hundred thousand or so gets tedious. There are other, much faster (though more verbose) algorithms that ''could'' be used. This algorithm '''is''' well suited to finding '''arbitrary''' attractive numbers though.
use Lingua::EN::Numbers;
use ntheory:from<Perl5> <factor is_prime>;
sub display ($n,$m) { ($n..$m).grep: (~*).&factor.elems.&is_prime }
sub count ($n,$m) { +($n..$m).grep: (~*).&factor.elems.&is_prime }
# The Task
put "Attractive numbers from 1 to 120:\n" ~
display(1, 120)».fmt("%3d").rotor(20, :partial).join: "\n";
# Robusto!
for 1, 1000, 1, 10000, 1, 100000, 2**73 + 1, 2**73 + 100 -> $a, $b {
put "\nCount of attractive numbers from {comma $a} to {comma $b}:\n" ~
comma count $a, $b
}
{{out}}
Attractive numbers from 1 to 120:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
Count of attractive numbers from 1 to 1,000:
636
Count of attractive numbers from 1 to 10,000:
6,396
Count of attractive numbers from 1 to 100,000:
63,255
Count of attractive numbers from 9,444,732,965,739,290,427,393 to 9,444,732,965,739,290,427,492:
58
Phix
function attractive(integer lim)
sequence s = {}
for i=1 to lim do
integer n = length(prime_factors(i,true))
if is_prime(n) then s &= i end if
end for
return s
end function
sequence s = attractive(120)
printf(1,"There are %d attractive numbers up to and including %d:\n",{length(s),120})
pp(s,{pp_IntCh,false})
for i=3 to 6 do
atom t0 = time()
integer p = power(10,i),
l = length(attractive(p))
string e = elapsed(time()-t0)
printf(1,"There are %,d attractive numbers up to %,d (%s)\n",{l,p,e})
end for
{{out}}
There are 74 attractive numbers up to and including 120:
{4,6,8,9,10,12,14,15,18,20,21,22,25,26,27,28,30,32,33,34,35,38,39,42,44,45,
46,48,49,50,51,52,55,57,58,62,63,65,66,68,69,70,72,74,75,76,77,78,80,82,85,
86,87,91,92,93,94,95,98,99,102,105,106,108,110,111,112,114,115,116,117,118,
119,120}
There are 636 attractive numbers up to 1,000 (0s)
There are 6,396 attractive numbers up to 10,000 (0.0s)
There are 63,255 attractive numbers up to 100,000 (0.3s)
There are 617,552 attractive numbers up to 1,000,000 (4.1s)
Python
Procedural
{{Works with|Python|2.7.12}}
from sympy import sieve # library for primes
def get_pfct(n):
i = 2; factors = []
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.append(i)
if n > 1:
factors.append(n)
return len(factors)
sieve.extend(110) # first 110 primes...
primes=sieve._list
pool=[]
for each in xrange(0,121):
pool.append(get_pfct(each))
for i,each in enumerate(pool):
if each in primes:
print i,
{{out}}
4,6,8,9,10,12,14,15,18,20,21,22,25,26,27,28,30,32,33,34,35,38,39,42,44,45,46, 48,49,50,51,52,55,57,58,62,63,65,66,68,69,70,72,74,75,76,77,78,80,82,85,86,87, 91,92,93,94,95,98,99,102,105,106,108,110,111,112,114,115,116,117,118,119,120
Functional
Without importing a primes library – at this scale a light and visible implementation is more than enough, and provides more material for comparison. {{Works with|Python|3.7}}
'''Attractive numbers'''
from itertools import chain, count, takewhile
from functools import reduce
# attractiveNumbers :: () -> [Int]
def attractiveNumbers():
'''A non-finite stream of attractive numbers.
(OEIS A063989)
'''
return filter(
compose(
isPrime,
len,
primeDecomposition
),
count(1)
)
# TEST ----------------------------------------------------
def main():
'''Attractive numbers drawn from the range [1..120]'''
for row in chunksOf(15)(list(
takewhile(
lambda x: 120 >= x,
attractiveNumbers()
)
)):
print(' '.join(map(
compose(justifyRight(3)(' '), str),
row
)))
# GENERAL FUNCTIONS ---------------------------------------
# chunksOf :: Int -> [a] -> [[a]]
def chunksOf(n):
'''A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
divible, the final list will be shorter than n.
'''
return lambda xs: reduce(
lambda a, i: a + [xs[i:n + i]],
range(0, len(xs), n), []
) if 0 < n else []
# compose :: ((a -> a), ...) -> (a -> a)
def compose(*fs):
'''Composition, from right to left,
of a series of functions.
'''
return lambda x: reduce(
lambda a, f: f(a),
fs[::-1], x
)
# We only need light implementations
# of prime functions here:
# primeDecomposition :: Int -> [Int]
def primeDecomposition(n):
'''List of integers representing the
prime decomposition of n.
'''
def go(n, p):
return [p] + go(n // p, p) if (
0 == n % p
) else []
return list(chain.from_iterable(map(
lambda p: go(n, p) if isPrime(p) else [],
range(2, 1 + n)
)))
# isPrime :: Int -> Bool
def isPrime(n):
'''True if n is prime.'''
if n in (2, 3):
return True
if 2 > n or 0 == n % 2:
return False
if 9 > n:
return True
if 0 == n % 3:
return False
return not any(map(
lambda x: 0 == n % x or 0 == n % (2 + x),
range(5, 1 + int(n ** 0.5), 6)
))
# justifyRight :: Int -> Char -> String -> String
def justifyRight(n):
'''A string padded at left to length n,
using the padding character c.
'''
return lambda c: lambda s: s.rjust(n, c)
# MAIN ---
if __name__ == '__main__':
main()
{{Out}}
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27
28 30 32 33 34 35 38 39 42 44 45 46 48 49 50
51 52 55 57 58 62 63 65 66 68 69 70 72 74 75
76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
Racket
#lang racket
(require math/number-theory)
(define attractive? (compose1 prime? prime-omega))
(filter attractive? (range 1 121))
{{out}}
(4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34 35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68 69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99 102 105 106 108 110 111 112 114 115 116 117 118 119 120)
REXX
Programming notes: The use of a table that contains some low primes is one fast method to test for primality of the
various prime factors.
The '''cFact''' (count factors) function is optimized way beyond what this task requires, and it can be optimized
further by expanding the '''do while'''s clauses (lines 3──►6 in the '''cFact''' function).
/*REXX program finds and shows lists (or counts) attractive numbers up to a specified N.*/
parse arg N . /*get optional argument from the C.L. */
if N=='' | N=="," then N= 120 /*Not specified? Then use the default.*/
cnt= N<0 /*semaphore used to control the output.*/
N= abs(N) /*ensure that N is a positive number.*/
call genP 100 /*gen 100 primes (high= 541); overkill.*/
sw= linesize() - 1 /*SW: is the usable screen width. */
if \cnt then say 'attractive numbers up to and including ' N " are:"
#= 0 /*number of attractive #'s (so far). */
$= /*a list of attractive numbers (so far)*/
do j=1 for N; if @.j then iterate /*Is it a prime? Then skip the number.*/
a= cFact(j) /*call cFact to count the factors in J.*/
if \@.a then iterate /*if # of factors not prime, then skip.*/
#= # + 1 /*add the index and number of factors.*/
if cnt then iterate /*if not displaying numbers, skip list.*/
_= $ j /*append a number to $ list.*/
if length(_)>sw then do; say strip($); $= j; end /*display a line of numbers.*/
else $= _ /*append the latest number. */
end /*j*/
if $\=='' & \cnt then say strip($) /*display any residual numbers in list.*/
say; say # ' attractive numbers found up to and including ' N
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
cFact: procedure; parse arg z 1 oz; if z<2 then return z /*if Z too small, return Z.*/
#= 0 /*#: is the number of factors (so far)*/
do while z//2==0; #= #+1; z= z%2; end /*maybe add the factor of two. */
do while z//3==0; #= #+1; z= z%3; end /* " " " " " three.*/
do while z//5==0; #= #+1; z= z%5; end /* " " " " " five. */
do while z//7==0; #= #+1; z= z%7; end /* " " " " " seven.*/
/* [↑] reduce Z by some low primes. */
do k=11 by 6 while k<=z /*insure that K isn't divisible by 3.*/
parse var k '' -1 _ /*obtain the last decimal digit of K. */
if _\==5 then do while z//k==0; #= #+1; z= z%k; end /*maybe reduce Z.*/
if _ ==3 then iterate /*Next number ÷ by 5? Skip. ____ */
if k*k>oz then leave /*are we greater than the √ OZ ? */
y= k + 2 /*get next divisor, hopefully a prime.*/
do while z//y==0; #= #+1; z= z%y; end /*maybe reduce Z.*/
end /*k*/
if z\==1 then return # + 1 /*if residual isn't unity, then add it.*/
return # /*return the number of factors in OZ. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: procedure expose @.; parse arg n; @.=0; @.2= 1; @.3= 1; p= 2
do j=3 by 2 until p==n; do k=3 by 2 until k*k>j; if j//k==0 then iterate j
end /*k*/; @.j = 1; p= p + 1
end /*j*/; return /* [↑] generate N primes. */
This REXX program makes use of '''LINESIZE''' REXX program (or BIF) which is used to determine the screen width (or linesize) of the terminal (console).
Some REXXes don't have this BIF. It is used here to automatically/idiomatically limit the width of the output list.
The '''LINESIZE.REX''' REXX program is included here ───► [[LINESIZE.REX]].
{{out|output|text= when using the default input:}}
attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34 35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68 69 70 72 74
75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99 102 105 106 108 110 111 112 114 115 116 117 118 119 120
74 attractive numbers found up to and including 120
{{out|output|text= when using the input of: -10000 }}
6396 attractive numbers found up to and including 10000
{{out|output|text= when using the input of: -100000 }}
63255 attractive numbers found up to and including 100000
{{out|output|text= when using the input of: -1000000 }}
623232 attractive numbers found up to and including 1000000
Ring
# Project: Attractive Numbers
decomp = []
nump = 0
see "Attractive Numbers up to 120:" + nl
while nump < 120
decomp = []
nump = nump + 1
for i = 1 to nump
if isPrime(i) and nump%i = 0
add(decomp,i)
dec = nump/i
while dec%i = 0
add(decomp,i)
dec = dec/i
end
ok
next
if isPrime(len(decomp))
see string(nump) + " = ["
for n = 1 to len(decomp)
if n < len(decomp)
see string(decomp[n]) + "*"
else
see string(decomp[n]) + "] - " + len(decomp) + " is prime" + nl
ok
next
ok
end
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
{{out}}
Attractive Numbers up to 120:
4 = [2*2] - 2 is prime
6 = [2*3] - 2 is prime
8 = [2*2*2] - 3 is prime
9 = [3*3] - 2 is prime
10 = [2*5] - 2 is prime
12 = [2*2*3] - 3 is prime
14 = [2*7] - 2 is prime
15 = [3*5] - 2 is prime
18 = [2*3*3] - 3 is prime
20 = [2*2*5] - 3 is prime
...
...
...
102 = [2*3*17] - 3 is prime
105 = [3*5*7] - 3 is prime
106 = [2*53] - 2 is prime
108 = [2*2*3*3*3] - 5 is prime
110 = [2*5*11] - 3 is prime
111 = [3*37] - 2 is prime
112 = [2*2*2*2*7] - 5 is prime
114 = [2*3*19] - 3 is prime
115 = [5*23] - 2 is prime
116 = [2*2*29] - 3 is prime
117 = [3*3*13] - 3 is prime
118 = [2*59] - 2 is prime
119 = [7*17] - 2 is prime
120 = [2*2*2*3*5] - 5 is prime
Ruby
require "prime"
p (1..120).select{|n| n.prime_division.sum(&:last).prime? }
{{out}}
[4, 6, 8, 9, 10, 12, 14, 15, 18, 20, 21, 22, 25, 26, 27, 28, 30, 32, 33, 34, 35, 38, 39, 42, 44, 45, 46, 48, 49, 50, 51, 52, 55, 57, 58, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 102, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120]
Rust
Uses [https://crates.io/crates/primal primal]
use primal::Primes;
const MAX: u64 = 120;
/// Returns an Option with a tuple => Ok((smaller prime factor, num divided by that prime factor))
/// If num is a prime number itself, returns None
fn extract_prime_factor(num: u64) -> Option<(u64, u64)> {
let mut i = 0;
if primal::is_prime(num) {
None
} else {
loop {
let prime = Primes::all().nth(i).unwrap() as u64;
if num % prime == 0 {
return Some((prime, num / prime));
} else {
i += 1;
}
}
}
}
/// Returns a vector containing all the prime factors of num
fn factorize(num: u64) -> Vec<u64> {
let mut factorized = Vec::new();
let mut rest = num;
while let Some((prime, factorizable_rest)) = extract_prime_factor(rest) {
factorized.push(prime);
rest = factorizable_rest;
}
factorized.push(rest);
factorized
}
fn main() {
let mut output: Vec<u64> = Vec::new();
for num in 4 ..= MAX {
if primal::is_prime(factorize(num).len() as u64) {
output.push(num);
}
}
println!("The attractive numbers up to and including 120 are\n{:?}", output);
}
{{out}}
The attractive numbers up to and including 120 are
[4, 6, 8, 9, 10, 12, 14, 15, 18, 20, 21, 22, 25, 26, 27, 28, 30, 32, 33, 34, 35, 38, 39, 42, 44, 45, 46, 48, 49, 50, 51, 52, 55, 57, 58, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 102, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120]
Scala
{{Out}}Best seen in running your browser either by [https://scalafiddle.io/sf/23oE3SQ/0 ScalaFiddle (ES aka JavaScript, non JVM)] or [https://scastie.scala-lang.org/U0QUQu0uTT24vbDEHU1c0Q Scastie (remote JVM)].
object AttractiveNumbers extends App {
private val max = 120
private var count = 0
private def nFactors(n: Int): Int = {
@scala.annotation.tailrec
def factors(x: Int, f: Int, acc: Int): Int =
if (f * f > x) acc + 1
else
x % f match {
case 0 => factors(x / f, f, acc + 1)
case _ => factors(x, f + 1, acc)
}
factors(n, 2, 0)
}
private def ls: Seq[String] =
for (i <- 4 to max;
n = nFactors(i)
if n >= 2 && nFactors(n) == 1 // isPrime(n)
) yield f"$i%4d($n)"
println(f"The attractive numbers up to and including $max%d are: [number(factors)]\n")
ls.zipWithIndex
.groupBy { case (_, index) => index / 20 }
.foreach { case (_, row) => println(row.map(_._1).mkString) }
}
Sidef
func is_attractive(n) {
n.bigomega.is_prime
}
1..120 -> grep(is_attractive).say
{{out}}
[4, 6, 8, 9, 10, 12, 14, 15, 18, 20, 21, 22, 25, 26, 27, 28, 30, 32, 33, 34, 35, 38, 39, 42, 44, 45, 46, 48, 49, 50, 51, 52, 55, 57, 58, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 102, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120]
Visual Basic .NET
{{trans|D}}
Module Module1
Const MAX = 120
Function IsPrime(n As Integer) As Boolean
If n < 2 Then Return False
If n Mod 2 = 0 Then Return n = 2
If n Mod 3 = 0 Then Return n = 3
Dim d = 5
While d * d <= n
If n Mod d = 0 Then Return False
d += 2
If n Mod d = 0 Then Return False
d += 4
End While
Return True
End Function
Function PrimefactorCount(n As Integer) As Integer
If n = 1 Then Return 0
If IsPrime(n) Then Return 1
Dim count = 0
Dim f = 2
While True
If n Mod f = 0 Then
count += 1
n /= f
If n = 1 Then Return count
If IsPrime(n) Then f = n
ElseIf f >= 3 Then
f += 2
Else
f = 3
End If
End While
Throw New Exception("Unexpected")
End Function
Sub Main()
Console.WriteLine("The attractive numbers up to and including {0} are:", MAX)
Dim i = 1
Dim count = 0
While i <= MAX
Dim n = PrimefactorCount(i)
If IsPrime(n) Then
Console.Write("{0,4}", i)
count += 1
If count Mod 20 = 0 Then
Console.WriteLine()
End If
End If
i += 1
End While
Console.WriteLine()
End Sub
End Module
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120
zkl
Using GMP (GNU Multiple Precision Arithmetic Library, probabilistic primes) because it is easy and fast to test for primeness.
var [const] BI=Import("zklBigNum"); // libGMP
fcn attractiveNumber(n){ BI(primeFactors(n).len()).probablyPrime() }
println("The attractive numbers up to and including 120 are:");
[1..120].filter(attractiveNumber)
.apply("%4d".fmt).pump(Void,T(Void.Read,19,False),"println");
Using [[Prime decomposition#zkl]]
fcn primeFactors(n){ // Return a list of factors of n
acc:=fcn(n,k,acc,maxD){ // k is 2,3,5,7,9,... not optimum
if(n==1 or k>maxD) acc.close();
else{
q,r:=n.divr(k); // divr-->(quotient,remainder)
if(r==0) return(self.fcn(q,k,acc.write(k),q.toFloat().sqrt()));
return(self.fcn(n,k+1+k.isOdd,acc,maxD))
}
}(n,2,Sink(List),n.toFloat().sqrt());
m:=acc.reduce('*,1); // mulitply factors
if(n!=m) acc.append(n/m); // opps, missed last factor
else acc;
}
{{out}}
The attractive numbers up to and including 120 are:
4 6 8 9 10 12 14 15 18 20 21 22 25 26 27 28 30 32 33 34
35 38 39 42 44 45 46 48 49 50 51 52 55 57 58 62 63 65 66 68
69 70 72 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99
102 105 106 108 110 111 112 114 115 116 117 118 119 120