Attractive numbers
You are encouraged to solve this task according to the task description, using any language you may know.
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: A063989: Numbers with a prime number of prime divisors.
11l
<lang 11l>F is_prime(n)
I n < 2
R 0B
L(i) 2 .. Int(sqrt(n))
I n % i == 0
R 0B
R 1B
F get_pfct(=n)
V i = 2
[Int] factors
L i * i <= n
I n % i
i++
E
n I/= i
factors.append(i)
I n > 1
factors.append(n)
R factors.len
[Int] pool
L(each) 0..120
pool.append(get_pfct(each))
[Int] r L(each) pool
I is_prime(each)
r.append(L.index)
print(r.map(String).join(‘,’))</lang>
- Output:
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
8080 Assembly
<lang 8080asm> ;;; Show attractive numbers up to 120 MAX: equ 120 ; can be up to 255 (8 bit math is used) ;;; CP/M calls puts: equ 9 bdos: equ 5 org 100h ;;; -- Zero memory ------------------------------------------------ lxi b,fctrs ; page 2 mvi e,2 ; zero out two pages xra a mov d,a zloop: stax b inx b dcr d jnz zloop dcr e jnz zloop ;;; -- Generate primes -------------------------------------------- lxi h,plist ; pointer to beginning of primes list mvi e,2 ; first prime is 2 pstore: mov m,e ; begin prime list pcand: inr e ; next candidate jz factor ; if 0, we've rolled over, so we're done mov l,d ; beginning of primes list (D=0 here) mov c,m ; C = prime to test against ptest: mov a,e ploop: sub c ; test by repeated subtraction jc notdiv ; if carry, not divisible jz pcand ; if zero, next candidate jmp ploop notdiv: inx h ; get next prime mov c,m mov a,c ; is it zero? ora a jnz ptest ; if not, test against next prime jmp pstore ; otherwise, add E to the list of primes ;;; -- Count factors ---------------------------------------------- factor: mvi c,2 ; start with two fnum: mvi a,MAX ; is candidate beyond maximum? cmp c jc output ; then stop mvi d,0 ; D = number of factors of C mov l,d ; L = first prime mov e,c ; E = number we're factorizing fprim: mvi h,ppage ; H = current prime mov h,m ftest: mvi b,0 mov a,e cpi 1 ; If one, we've counted all the factors jz nxtfac fdiv: sub h jz divi jc ndivi inr b jmp fdiv divi: inr d ; we found a factor inr b mov e,b ; we've removed it, try again jmp ftest ndivi: inr l ; not divisible, try next prime jmp fprim nxtfac: mov a,d ; store amount of factors mvi b,fcpage stax b inr c ; do next number jmp fnum ;;; -- Check which numbers are attractive and print them ---------- output: lxi b,fctrs+2 ; start with two mvi h,ppage ; H = page of primes onum: mvi a,MAX ; is candidate beyond maximum? cmp c rc ; then stop ldax b ; get amount of factors mvi l,0 ; start at beginning of prime list chprm: cmp m ; check against current prime jz print ; if it's prime, then print the number inr l ; otherwise, check next prime jp chprm next: inr c ; check next number jmp onum print: push b ; keep registers push h mov a,c ; print number call printa pop h ; restore registers pop b jmp next ;;; Subroutine: print the number in A printa: lxi d,num ; DE = string mvi b,10 ; divisor digit: mvi c,-1 ; C = quotient divlp: inr c sub b jnc divlp adi '0'+10 ; make digit dcx d ; store digit stax d mov a,c ; again with new quotient ora a ; is it zero? jnz digit ; if not, do next digit mvi c,puts ; CP/M print string (in DE) jmp bdos db '000' ; placeholder for number num: db ' $' fcpage: equ 2 ; factors in page 2 ppage: equ 3 ; primes in page 3 fctrs: equ 256*fcpage plist: equ 256*ppage</lang>
- Output:
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
Ada
<lang Ada>with Ada.Text_IO;
procedure Attractive_Numbers is
function Is_Prime (N : in Natural) return Boolean is
D : Natural := 5;
begin
if N < 2 then return False; end if;
if N mod 2 = 0 then return N = 2; end if;
if N mod 3 = 0 then return N = 3; end if;
while D * D <= N loop
if N mod D = 0 then return False; end if;
D := D + 2;
if N mod D = 0 then return False; end if;
D := D + 4;
end loop;
return True;
end Is_Prime;
function Count_Prime_Factors (N : in Natural) return Natural is
NC : Natural := N;
Count : Natural := 0;
F : Natural := 2;
begin
if NC = 1 then return 0; end if;
if Is_Prime (NC) then return 1; end if;
loop
if NC mod F = 0 then
Count := Count + 1;
NC := NC / F;
if NC = 1 then
return Count;
end if;
if Is_Prime (NC) then F := NC; end if;
elsif F >= 3 then
F := F + 2;
else
F := 3;
end if;
end loop;
end Count_Prime_Factors;
procedure Show_Attractive (Max : in Natural)
is
use Ada.Text_IO;
package Integer_IO is
new Ada.Text_IO.Integer_IO (Integer);
N : Natural;
Count : Natural := 0;
begin
Put_Line ("The attractive numbers up to and including " & Max'Image & " are:");
for I in 1 .. Max loop
N := Count_Prime_Factors (I);
if Is_Prime (N) then
Integer_IO.Put (I, Width => 5);
Count := Count + 1;
if Count mod 20 = 0 then New_Line; end if;
end if;
end loop;
end Show_Attractive;
begin
Show_Attractive (Max => 120);
end Attractive_Numbers;</lang>
- 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
ALGOL W
<lang algolw>% find some attractive numbers - numbers whose prime factor count is prime % begin
% implements the sieve of Eratosthenes %
% s(i) is set to true if i is prime, false otherwise %
% algol W doesn't have a upb operator, so we pass the size of the %
% array in n %
procedure sieve( logical array s ( * ); integer value n ) ;
begin
% start with everything flagged as prime %
for i := 1 until n do s( i ) := true;
% sieve out the non-primes %
s( 1 ) := false;
for i := 2 until truncate( sqrt( n ) ) do begin
if s( i ) then for p := i * i step i until n do s( p ) := false
end for_i ;
end sieve ;
% returns the count of prime factors of n, using the sieve of primes s %
% n must be greater than 0 %
integer procedure countPrimeFactors ( integer value n; logical array s ( * ) ) ;
if s( n ) then 1
else begin
integer count, rest;
rest := n;
count := 0;
while rest rem 2 = 0 do begin
count := count + 1;
rest := rest div 2
end while_divisible_by_2 ;
for factor := 3 step 2 until n - 1 do begin
if s( factor ) then begin
while rest > 1 and rest rem factor = 0 do begin
count := count + 1;
rest := rest div factor
end while_divisible_by_factor
end if_prime_factor
end for_factor ;
count
end countPrimeFactors ;
% maximum number for the task %
integer maxNumber;
maxNumber := 120;
% show the attractive numbers %
begin
logical array s ( 1 :: maxNumber );
sieve( s, maxNumber );
i_w := 2; % set output field width %
s_w := 1; % and output separator width %
% find and display the attractive numbers %
for i := 2 until maxNumber do if s( countPrimeFactors( i, s ) ) then writeon( i )
end
end.</lang>
- Output:
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
AppleScript
<lang applescript>on isPrime(n)
if (n < 4) then return (n > 1)
if ((n mod 2 is 0) or (n mod 3 is 0)) then return false
repeat with i from 5 to (n ^ 0.5) div 1 by 6
if ((n mod i is 0) or (n mod (i + 2) is 0)) then return false
end repeat
return true
end isPrime
on primeFactorCount(n)
set x to n
set counter to 0
if (n > 1) then
repeat while (n mod 2 = 0)
set counter to counter + 1
set n to n div 2
end repeat
repeat while (n mod 3 = 0)
set counter to counter + 1
set n to n div 3
end repeat
set i to 5
set limit to (n ^ 0.5) div 1
repeat until (i > limit)
repeat while (n mod i = 0)
set counter to counter + 1
set n to n div i
end repeat
tell (i + 2) to repeat while (n mod it = 0)
set counter to counter + 1
set n to n div it
end repeat
set i to i + 6
set limit to (n ^ 0.5) div 1
end repeat
if (n > 1) then set counter to counter + 1
end if
return counter
end primeFactorCount
-- Task code: local output, n set output to {} repeat with n from 1 to 120
if (isPrime(primeFactorCount(n))) then set end of output to n
end repeat return output</lang>
- Output:
<lang applescript>{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}</lang>
It's possible of course to dispense with the isPrime() handler and instead use primeFactorCount() to count the prime factors of its own output, with 1 indicating an attractive number. The loss of performance only begins to become noticeable in the unlikely event of needing 300,000 or more such numbers!
Arturo
<lang rebol>attractive?: function [x] -> prime? size factors.prime x
print select 1..120 => attractive?</lang>
- Output:
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
AWK
<lang 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)
} </lang>
- Output:
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
BASIC
<lang basic>10 DEFINT A-Z 20 M=120 30 DIM C(M): C(0)=-1: C(1)=-1 40 FOR I=2 TO SQR(M) 50 IF NOT C(I) THEN FOR J=I+I TO M STEP I: C(J)=-1: NEXT 60 NEXT 70 FOR I=2 TO M 80 N=I: C=0 90 FOR J=2 TO M 100 IF NOT C(J) THEN IF N MOD J=0 THEN N=N\J: C=C+1: GOTO 100 110 NEXT 120 IF NOT C(C) THEN PRINT I, 130 NEXT</lang>
- Output:
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
<lang c>#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;
}</lang>
- 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
C#
<lang csharp>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();
}
}
}</lang>
- 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
C++
<lang cpp>#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;
}</lang>
- 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
D
<lang d>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;
}</lang>
- 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
Delphi
See #Pascal.
F#
<lang Fsharp>// attractive_numbers.fsx // taken from Primality by trial division let rec primes =
let next_state s = Some(s, s + 2)
Seq.cache
(Seq.append
(seq[ 2; 3; 5 ])
(Seq.unfold next_state 7
|> Seq.filter is_prime))
and is_prime number =
let rec is_prime_core number current limit =
let cprime = primes |> Seq.item current
if cprime >= limit then true
elif number % cprime = 0 then false
else is_prime_core number (current + 1) (number/cprime)
if number = 2 then true
elif number < 2 then false
else is_prime_core number 0 number
// taken from Prime decomposition task and modified to add let count_prime_divisors n =
let rec loop c n count =
let p = Seq.item n primes
if c < (p * p) then count
elif c % p = 0 then loop (c / p) n (count + 1)
else loop c (n + 1) count
loop n 0 1
let is_attractive = count_prime_divisors >> is_prime let print_iter i n =
if i % 10 = 9 then printfn "%d" n else printf "%d\t" n
[1..120] |> List.filter is_attractive |> List.iteri print_iter </lang>
- Output:
>dotnet fsi attractive_numbers.fsx 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
<lang factor>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</lang>
- 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
Fortran
<lang fortran> program attractive_numbers
use iso_fortran_env, only: output_unit implicit none
integer, parameter :: maximum=120, line_break=20 integer :: i, counter
write(output_unit,'(A,x,I0,x,A)') "The attractive numbers up to and including", maximum, "are:"
counter = 0
do i = 1, maximum
if (is_prime(count_prime_factors(i))) then
write(output_unit,'(I0,x)',advance="no") i
counter = counter + 1
if (modulo(counter, line_break) == 0) write(output_unit,*)
end if
end do
write(output_unit,*)
contains
pure function is_prime(n)
integer, intent(in) :: n
logical :: is_prime
integer :: d
is_prime = .false.
d = 5
if (n < 2) return
if (modulo(n, 2) == 0) then
is_prime = n==2
return
end if
if (modulo(n, 3) == 0) then
is_prime = n==3
return
end if
do
if (d**2 > n) then
is_prime = .true.
return
end if
if (modulo(n, d) == 0) then
is_prime = .false.
return
end if
d = d + 2
if (modulo(n, d) == 0) then
is_prime = .false.
return
end if
d = d + 4
end do
is_prime = .true. end function is_prime
pure function count_prime_factors(n)
integer, intent(in) :: n
integer :: count_prime_factors
integer :: i, f
count_prime_factors = 0
if (n == 1) return
if (is_prime(n)) then
count_prime_factors = 1
return
end if
count_prime_factors = 0
f = 2
i = n
do
if (modulo(i, f) == 0) then
count_prime_factors = count_prime_factors + 1
i = i/f
if (i == 1) exit
if (is_prime(i)) f = i
else if (f >= 3) then
f = f + 2
else
f = 3
end if
end do
end function count_prime_factors
end program attractive_numbers </lang>
- 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
FreeBASIC
<lang freebasic> 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 </lang>
- Output:
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. <lang go>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()
}</lang>
- 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
Groovy
<lang groovy>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()
}
}</lang>
- 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
Haskell
<lang 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</lang>
Or equivalently, as a list comprehension: <lang haskell>import Data.Numbers.Primes
attractiveNumbers :: [Integer] attractiveNumbers =
[ x | x <- [1 ..] , isPrime (length (primeFactors x)) ]
main :: IO () main = print $ takeWhile (<= 120) attractiveNumbers</lang>
Or simply: <lang haskell>import Data.Numbers.Primes
attractiveNumbers :: [Integer] attractiveNumbers =
filter (isPrime . length . primeFactors) [1 ..]
main :: IO () main = print $ takeWhile (<= 120) attractiveNumbers</lang>
- Output:
[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]
J
<lang j> echo (#~ (1 p: ])@#@q:) >:i.120 </lang>
- Output:
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
JavaScript
<lang javascript>(() => {
'use strict';
// attractiveNumbers :: () -> Gen [Int]
const attractiveNumbers = () =>
// An infinite series of attractive numbers.
filter(
compose(isPrime, length, primeFactors)
)(enumFrom(1));
// ----------------------- TEST -----------------------
// main :: IO ()
const main = () =>
showCols(10)(
takeWhile(ge(120))(
attractiveNumbers()
)
);
// ---------------------- PRIMES ----------------------
// isPrime :: Int -> Bool
const isPrime = n => {
// True if n is prime.
if (2 === n || 3 === n) {
return true
}
if (2 > n || 0 === n % 2) {
return false
}
if (9 > n) {
return true
}
if (0 === n % 3) {
return false
}
return !enumFromThenTo(5)(11)(
1 + Math.floor(Math.pow(n, 0.5))
).some(x => 0 === n % x || 0 === n % (2 + x));
};
// primeFactors :: Int -> [Int]
const primeFactors = n => {
// A list of the prime factors of n.
const
go = x => {
const
root = Math.floor(Math.sqrt(x)),
m = until(
([q, _]) => (root < q) || (0 === (x % q))
)(
([_, r]) => [step(r), 1 + r]
)([
0 === x % 2 ? (
2
) : 3,
1
])[0];
return m > root ? (
[x]
) : ([m].concat(go(Math.floor(x / m))));
},
step = x => 1 + (x << 2) - ((x >> 1) << 1);
return go(n);
};
// ---------------- GENERIC FUNCTIONS -----------------
// chunksOf :: Int -> [a] -> a const chunksOf = n => xs => enumFromThenTo(0)(n)( xs.length - 1 ).reduce( (a, i) => a.concat([xs.slice(i, (n + i))]), [] );
// compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
const compose = (...fs) =>
fs.reduce(
(f, g) => x => f(g(x)),
x => x
);
// enumFrom :: Enum a => a -> [a]
function* enumFrom(x) {
// A non-finite succession of enumerable
// values, starting with the value x.
let v = x;
while (true) {
yield v;
v = 1 + v;
}
}
// enumFromThenTo :: Int -> Int -> Int -> [Int]
const enumFromThenTo = x1 =>
x2 => y => {
const d = x2 - x1;
return Array.from({
length: Math.floor(y - x2) / d + 2
}, (_, i) => x1 + (d * i));
};
// filter :: (a -> Bool) -> Gen [a] -> [a]
const filter = p => xs => {
function* go() {
let x = xs.next();
while (!x.done) {
let v = x.value;
if (p(v)) {
yield v
}
x = xs.next();
}
}
return go(xs);
};
// ge :: Ord a => a -> a -> Bool
const ge = x =>
// True if x >= y
y => x >= y;
// justifyRight :: Int -> Char -> String -> String
const justifyRight = n =>
// The string s, preceded by enough padding (with
// the character c) to reach the string length n.
c => s => n > s.length ? (
s.padStart(n, c)
) : s;
// last :: [a] -> a
const last = xs =>
// The last item of a list.
0 < xs.length ? xs.slice(-1)[0] : undefined;
// length :: [a] -> Int
const length = xs =>
// Returns Infinity over objects without finite
// length. This enables zip and zipWith to choose
// the shorter argument when one is non-finite,
// like cycle, repeat etc
(Array.isArray(xs) || 'string' === typeof xs) ? (
xs.length
) : Infinity;
// map :: (a -> b) -> [a] -> [b]
const map = f =>
// The list obtained by applying f
// to each element of xs.
// (The image of xs under f).
xs => (
Array.isArray(xs) ? (
xs
) : xs.split()
).map(f);
// showCols :: Int -> [a] -> String
const showCols = w => xs => {
const
ys = xs.map(str),
mx = last(ys).length;
return unlines(chunksOf(w)(ys).map(
row => row.map(justifyRight(mx)(' ')).join(' ')
))
};
// str :: a -> String
const str = x =>
x.toString();
// takeWhile :: (a -> Bool) -> Gen [a] -> [a]
const takeWhile = p => xs => {
const ys = [];
let
nxt = xs.next(),
v = nxt.value;
while (!nxt.done && p(v)) {
ys.push(v);
nxt = xs.next();
v = nxt.value
}
return ys;
};
// unlines :: [String] -> String
const unlines = xs =>
// A single string formed by the intercalation
// of a list of strings with the newline character.
xs.join('\n');
// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = p => f => x => {
let v = x;
while (!p(v)) v = f(v);
return v;
};
// MAIN --- return main();
})();</lang>
- Output:
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
<lang java>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();
}
}</lang>
- 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
jq
Works with gojq, the Go implementation of jq
This entry uses:
- `is_prime` as defined at Erdős primes on RC
- `prime_factors` as defined at Smith numbers on RC
<lang jq> def count(s): reduce s as $x (null; .+1);
def is_attractive:
count(prime_factors) | is_prime;
def printattractive($m; $n):
"The attractive numbers from \($m) to \($n) are:\n", [range($m; $n+1) | select(is_attractive)];
printattractive(1; 120)</lang>
- Output:
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]
Julia
<lang 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)
</lang>
- Output:
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
<lang scala>// 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()
}</lang>
- 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
<lang 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" }</lang>
- 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
Lua
<lang 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</lang>
- Output:
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
<lang 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);</lang>
- Output:
[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]
Mathematica / Wolfram Language
<lang Mathematica>ClearAll[AttractiveNumberQ] AttractiveNumberQ[n_Integer] := FactorInteger[n]All, 2 // Total // PrimeQ Reap[Do[If[AttractiveNumberQ[i], Sow[i]], {i, 120}]]2, 1</lang>
- Output:
{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}
Nanoquery
<lang Nanoquery>MAX = 120
def is_prime(n) d = 5 if (n < 2) return false end if (n % 2) = 0 return n = 2 end if (n % 3) = 0 return n = 3 end
while (d * d) <= n if n % d = 0 return false end d += 2 if n % d = 0 return false end d += 4 end
return true end
def count_prime_factors(n) count = 0; f = 2 if n = 1 return 0 end if is_prime(n) return 1 end
while true if (n % f) = 0 count += 1 n /= f if n = 1 return count end if is_prime(n) f = n end else if f >= 3 f += 2 else f = 3 end end end
i = 0; n = 0; count = 0 println format("The attractive numbers up to and including %d are:\n", MAX) for i in range(1, MAX) n = count_prime_factors(i) if is_prime(n) print format("%4d", i) count += 1 if (count % 20) = 0 println end end end println</lang>
- 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
NewLisp
The factor function returns a list of the prime factors of an integer with repetition, e. g. (factor 12) is (2 2 3). <lang NewLisp> (define (prime? n) (= (length (factor n)) 1)) (define (attractive? n) (prime? (length (factor n))))
(filter attractive? (sequence 2 120)) </lang>
- Output:
(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
<lang Nim>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() </lang>
- 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
Pascal
same procedure as in http://rosettacode.org/wiki/Abundant,_deficient_and_perfect_number_classifications <lang pascal>program AttractiveNumbers; { numbers with count of factors = prime
- using modified sieve of erathosthes
- by adding the power of the prime to multiples
- of the composite number }
{$IFDEF FPC}
{$MODE DELPHI}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF} uses
sysutils;//timing
const
cTextMany = ' with many factors '; cText2 = ' with only two factors '; cText1 = ' with only one factor ';
type
tValue = LongWord; tpValue = ^tValue; tPower = array[0..63] of tValue;//2^64
var
power : tPower; sieve : array of byte;
function NextPotCnt(p: tValue):tValue; //return the first power <> 0 //power == n to base prim var
i : NativeUint;
begin
result := 0;
repeat
i := power[result];
Inc(i);
IF i < p then
BREAK
else
begin
i := 0;
power[result] := 0;
inc(result);
end;
until false;
power[result] := i;
inc(result);
end;
procedure InitSieveWith2; //the prime 2, because its the first one, is the one, //which can can be speed up tremendously, by moving var
pSieve : pByte; CopyWidth,lmt : NativeInt;
Begin
pSieve := @sieve[0]; Lmt := High(sieve); sieve[1] := 0; sieve[2] := 1; // aka 2^1 -> one factor CopyWidth := 2;
while CopyWidth*2 <= Lmt do Begin // copy idx 1,2 to 3,4 | 1..4 to 5..8 | 1..8 to 9..16 move(pSieve[1],pSieve[CopyWidth+1],CopyWidth); // 01 -> 0101 -> 01020102-> 0102010301020103 inc(CopyWidth,CopyWidth);//*2 //increment the factor of last element by one. inc(pSieve[CopyWidth]); //idx 12 1234 12345678 //value 01 -> 0102 -> 01020103-> 0102010301020104 end; //copy the rest move(pSieve[1],pSieve[CopyWidth+1],Lmt-CopyWidth);
//mark 0,1 not prime, 255 factors are today not possible 2^255 >> Uint64 sieve[0]:= 255; sieve[1]:= 255; sieve[2]:= 0; // make prime again
end;
procedure OutCntTime(T:TDateTime;txt:String;cnt:NativeInt); Begin
writeln(cnt:12,txt,T*86400:10:3,' s');
end;
procedure sievefactors; var
T0 : TDateTime; pSieve : pByte; i,j,i2,k,lmt,cnt : NativeUInt;
Begin
InitSieveWith2; pSieve := @sieve[0]; Lmt := High(sieve);
//Divide into 3 section
//first i*i*i<= lmt with time expensive NextPotCnt
T0 := now;
cnt := 0;
//third root of limit calculate only once, no comparison ala while i*i*i<= lmt do
k := trunc(exp(ln(Lmt)/3));
For i := 3 to k do
if pSieve[i] = 0 then
Begin
inc(cnt);
j := 2*i;
fillChar(Power,Sizeof(Power),#0);
Power[0] := 1;
repeat
inc(pSieve[j],NextPotCnt(i));
inc(j,i);
until j > lmt;
end;
OutCntTime(now-T0,cTextMany,cnt);
T0 := now;
//second i*i <= lmt
cnt := 0;
i := k+1;
k := trunc(sqrt(Lmt));
For i := i to k do
if pSieve[i] = 0 then
Begin
//first increment all multiples of prime by one
inc(cnt);
j := 2*i;
repeat
inc(pSieve[j]);
inc(j,i);
until j>lmt;
//second increment all multiples prime*prime by one
i2 := i*i;
j := i2;
repeat
inc(pSieve[j]);
inc(j,i2);
until j>lmt;
end;
OutCntTime(now-T0,cText2,cnt);
T0 := now;
//third i*i > lmt -> only one new factor
cnt := 0;
inc(k);
For i := k to Lmt shr 1 do
if pSieve[i] = 0 then
Begin
inc(cnt);
j := 2*i;
repeat
inc(pSieve[j]);
inc(j,i);
until j>lmt;
end;
OutCntTime(now-T0,cText1,cnt);
end;
const
smallLmt = 120; //needs 1e10 Byte = 10 Gb maybe someone got 128 Gb :-) nearly linear time BigLimit = 10*1000*1000*1000;
var
T0,T : TDateTime; i,cnt,lmt : NativeInt;
Begin
setlength(sieve,smallLmt+1);
sievefactors;
cnt := 0;
For i := 2 to smallLmt do
Begin
if sieve[sieve[i]] = 0 then
Begin
write(i:4);
inc(cnt);
if cnt>19 then
Begin
writeln;
cnt := 0;
end;
end;
end;
writeln;
writeln;
T0 := now;
setlength(sieve,BigLimit+1);
T := now;
writeln('time allocating : ',(T-T0) *86400 :8:3,' s');
sievefactors;
T := now-T;
writeln('time sieving : ',T*86400 :8:3,' s');
T:= now;
cnt := 0;
i := 0;
lmt := 10;
repeat
repeat
inc(i);
{IF sieve[sieve[i]] = 0 then inc(cnt); takes double time is not relevant}
inc(cnt,ORD(sieve[sieve[i]] = 0));
until i = lmt;
writeln(lmt:11,cnt:12);
lmt := 10*lmt;
until lmt >High(sieve);
T := now-T;
writeln('time counting : ',T*86400 :8:3,' s');
writeln('time total : ',(now-T0)*86400 :8:3,' s');
end.</lang>
- Output:
1 with many factors 0.000 s
2 with only two factors 0.000 s
13 with only one factor 0.000 s
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
time allocating : 1.079 s
324 with many factors 106.155 s
9267 with only two factors 33.360 s
234944631 with only one factor 60.264 s
time sieving : 200.813 s
10 5
100 60
1000 636
10000 6396
100000 63255
1000000 623232
10000000 6137248
100000000 60472636
1000000000 596403124
10000000000 5887824685
time counting : 6.130 s
time total : 208.022 s
real 3m28,044s
Perl
<lang perl>use ntheory <is_prime factor>;
is_prime +factor $_ and print "$_ " for 1..120;</lang>
- Output:
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
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
- Output:
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)
PHP
<lang php><?php
function isPrime ($x) {
if ($x < 2) return false;
if ($x < 4) return true;
if ($x % 2 == 0) return false;
for ($d = 3; $d < sqrt($x); $d++) {
if ($x % $d == 0) return false;
}
return true;
}
function countFacs ($n) {
$count = 0;
$divisor = 1;
if ($n < 2) return 0;
while (!isPrime($n)) {
while (!isPrime($divisor)) $divisor++;
while ($n % $divisor == 0) {
$n /= $divisor;
$count++;
}
$divisor++;
if ($n == 1) return $count;
}
return $count + 1;
}
for ($i = 1; $i <= 120; $i++) {
if (isPrime(countFacs($i))) echo $i." ";
}
?></lang>
- Output:
4 6 8 10 12 14 15 18 20 21 22 26 27 28 30 32 33 34 35 36 38 39 42 44 45 46 48 50 51 52 55 57 58 62 63 65 66 68 69 70 74 75 76 77 78 80 82 85 86 87 91 92 93 94 95 98 99 100 102 105 106 108 110 111 112 114 115 116 117 118 119 120
Prolog
<lang prolog>prime_factors(N, Factors):-
S is sqrt(N), prime_factors(N, Factors, S, 2).
prime_factors(1, [], _, _):-!. prime_factors(N, [P|Factors], S, P):-
P =< S, 0 is N mod P, !, M is N // P, prime_factors(M, Factors, S, P).
prime_factors(N, Factors, S, P):-
Q is P + 1, Q =< S, !, prime_factors(N, Factors, S, Q).
prime_factors(N, [N], _, _).
is_prime(2):-!. is_prime(N):-
0 is N mod 2, !, fail.
is_prime(N):-
N > 2, S is sqrt(N), \+is_composite(N, S, 3).
is_composite(N, S, P):-
P =< S, 0 is N mod P, !.
is_composite(N, S, P):-
Q is P + 2, Q =< S, is_composite(N, S, Q).
attractive_number(N):-
prime_factors(N, Factors), length(Factors, Len), is_prime(Len).
print_attractive_numbers(From, To, _):-
From > To, !.
print_attractive_numbers(From, To, C):-
(attractive_number(From) ->
writef('%4r', [From]),
(0 is C mod 20 -> nl ; true),
C1 is C + 1
;
C1 = C
),
Next is From + 1,
print_attractive_numbers(Next, To, C1).
main:-
print_attractive_numbers(1, 120, 1).</lang>
- Output:
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
PureBasic
<lang PureBasic>#MAX=120 Dim prime.b(#MAX) FillMemory(@prime(),#MAX,#True,#PB_Byte) : FillMemory(@prime(),2,#False,#PB_Byte) For i=2 To Int(Sqr(#MAX)) : n=i*i : While n<#MAX : prime(n)=#False : n+i : Wend : Next
Procedure.i pfCount(n.i)
Shared prime()
If n=1 : ProcedureReturn 0 : EndIf
If prime(n) : ProcedureReturn 1 : EndIf
count=0 : f=2
Repeat
If n%f=0 : count+1 : n/f
If n=1 : ProcedureReturn count : EndIf
If prime(n) : f=n : EndIf
ElseIf f>=3 : f+2
Else : f=3
EndIf
ForEver
EndProcedure
OpenConsole() PrintN("The attractive numbers up to and including "+Str(#MAX)+" are:") For i=1 To #MAX
If prime(pfCount(i))
Print(RSet(Str(i),4)) : count+1 : If count%20=0 : PrintN("") : EndIf
EndIf
Next PrintN("") : Input()</lang>
- 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
Python
Procedural
<lang Python>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,</lang>
- Output:
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.
<lang python>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()</lang>
- Output:
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
Quackery
primefactors is defined at Prime decomposition.
<lang Quackery> [ primefactors size
primefactors size 1 = ] is attractive ( n --> b )
120 times
[ i^ 1+ attractive if
[ i^ 1+ echo sp ] ]</lang>
- Output:
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
R
<lang rsplus> is_prime <- function(num) {
if (num < 2) return(FALSE)
if (num %% 2 == 0) return(num == 2)
if (num %% 3 == 0) return(num == 3)
d <- 5
while (d*d <= num) {
if (num %% d == 0) return(FALSE)
d <- d + 2
if (num %% d == 0) return(FALSE)
d <- d + 4
}
TRUE
}
count_prime_factors <- function(num) {
if (num == 1) return(0)
if (is_prime(num)) return(1)
count <- 0
f <- 2
while (TRUE) {
if (num %% f == 0) {
count <- count + 1
num <- num / f
if (num == 1) return(count)
if (is_prime(num)) f <- num
}
else if (f >= 3) f <- f + 2
else f <- 3
}
}
max <- 120 cat("The attractive numbers up to and including",max,"are:\n") count <- 0 for (i in 1:max) {
n <- count_prime_factors(i);
if (is_prime(n)) {
cat(i," ", sep = "")
count <- count + 1
}
} </lang>
- 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
Racket
<lang racket>#lang racket (require math/number-theory) (define attractive? (compose1 prime? prime-omega)) (filter attractive? (range 1 121))</lang>
- Output:
(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)
Raku
(formerly Perl 6)
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.
<lang perl6>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
}</lang>
- Output:
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
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 could be optimized
further by expanding the do whiles clauses (lines 3──►6 in the cFact function).
If the argument for the program is negative, only a count of attractive numbers up to and including │N│ is shown. <lang rexx>/*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 ' commas(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 low prime? Then skip number.*/
a= cFact(j) /*call cFact to count the factors in J.*/
if \@.a then iterate /*if # of factors not prime, then skip.*/
#= # + 1 /*bump number of attractive #'s found. */
if cnt then iterate /*if not displaying numbers, skip list.*/
cj= commas(j); _= $ cj /*append a commatized number to $ list.*/
if length(_)>sw then do; say strip($); $= cj; 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 commas(#) ' attractive numbers found up to and including ' commas(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 one*/
return # /*return the number of factors in OZ. */
/*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ? /*──────────────────────────────────────────────────────────────────────────────────────*/ 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. */</lang>
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.
- output 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
- output when using the input of: -10000
6,396 attractive numbers found up to and including 10,000
- output when using the input of: -100000
63,255 attractive numbers found up to and including 100,000
- output when using the input of: -1000000
623,232 attractive numbers found up to and including 1,000,000
Ring
<lang 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
</lang>
- Output:
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
<lang ruby>require "prime"
p (1..120).select{|n| n.prime_division.sum(&:last).prime? } </lang>
- Output:
[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 primal <lang rust>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);
}</lang>
- 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]
Scala
- Output:
Best seen in running your browser either by ScalaFiddle (ES aka JavaScript, non JVM) or Scastie (remote JVM).
<lang Scala>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) }
}</lang>
Sidef
<lang ruby>func is_attractive(n) {
n.bigomega.is_prime
}
1..120 -> grep(is_attractive).say</lang>
- Output:
[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]
Swift
<lang swift>import Foundation
extension BinaryInteger {
@inlinable
public var isAttractive: Bool {
return primeDecomposition().count.isPrime
}
@inlinable
public var isPrime: Bool {
if self == 0 || self == 1 {
return false
} else if self == 2 {
return true
}
let max = Self(ceil((Double(self).squareRoot())))
for i in stride(from: 2, through: max, by: 1) {
if self % i == 0 {
return false
}
}
return true }
@inlinable
public func primeDecomposition() -> [Self] {
guard self > 1 else { return [] }
func step(_ x: Self) -> Self {
return 1 + (x << 2) - ((x >> 1) << 1)
}
let maxQ = Self(Double(self).squareRoot()) var d: Self = 1 var q: Self = self & 1 == 0 ? 2 : 3
while q <= maxQ && self % q != 0 {
q = step(d)
d += 1
}
return q <= maxQ ? [q] + (self / q).primeDecomposition() : [self] }
}
let attractive = Array((1...).lazy.filter({ $0.isAttractive }).prefix(while: { $0 <= 120 }))
print("Attractive numbers up to and including 120: \(attractive)")</lang>
- Output:
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]
Tcl
<lang Tcl>proc isPrime {n} {
if {$n < 2} {
return 0
}
if {$n > 3} {
if {0 == ($n % 2)} {
return 0
}
for {set d 3} {($d * $d) <= $n} {incr d 2} {
if {0 == ($n % $d)} {
return 0
}
}
}
return 1 ;# no divisor found
}
proc cntPF {n} {
set cnt 0
while {0 == ($n % 2)} {
set n [expr {$n / 2}]
incr cnt
}
for {set d 3} {($d * $d) <= $n} {incr d 2} {
while {0 == ($n % $d)} {
set n [expr {$n / $d}]
incr cnt
}
}
if {$n > 1} {
incr cnt
}
return $cnt
}
proc showRange {lo hi} {
puts "Attractive numbers in range $lo..$hi are:"
set k 0
for {set n $lo} {$n <= $hi} {incr n} {
if {[isPrime [cntPF $n]]} {
puts -nonewline " [format %3s $n]"
incr k
}
if {$k >= 20} {
puts ""
set k 0
}
}
if {$k > 0} {
puts ""
}
} showRange 1 120</lang>
- Output:
Attractive numbers in range 1..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
Vala
<lang vala>bool is_prime(int n) {
var d = 5;
if (n < 2) return false;
if (n % 2 == 0) return n == 2;
if (n % 3 == 0) return n == 3;
while (d * d <= n) {
if (n % d == 0) return false;
d += 2;
if (n % d == 0) return false;
d += 4;
}
return true;
}
int count_prime_factors(int n) {
var count = 0;
var f = 2;
if (n == 1) return 0;
if (is_prime(n)) return 1;
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;
}
}
}
void main() {
const int MAX = 120;
var n = 0;
var count = 0;
stdout.printf(@"The attractive numbers up to and including $MAX are:\n");
for (int i = 1; i <= MAX; i++) {
n = count_prime_factors(i);
if (is_prime(n)) {
stdout.printf("%4d", i);
count++;
if (count % 20 == 0)
stdout.printf("\n");
}
}
stdout.printf("\n");
}</lang>
- 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
VBA
<lang VBA>Option Explicit
Public Sub AttractiveNumbers() Dim max As Integer, i As Integer, n As Integer
max = 120
For i = 1 To max
n = CountPrimeFactors(i) If IsPrime(n) Then Debug.Print i
Next i
End Sub
Public Function IsPrime(ByVal n As Integer) As Boolean Dim d As Integer
IsPrime = True d = 5
If n < 2 Then
IsPrime = False GoTo Finish
End If
If n Mod 2 = 0 Then
IsPrime = (n = 2) GoTo Finish
End If
If n Mod 3 = 0 Then
IsPrime = (n = 3) GoTo Finish
End If
While (d * d <= n)
If (n Mod d = 0) Then IsPrime = False d = d + 2 If (n Mod d = 0) Then IsPrime = False d = d + 4
Wend Finish: End Function
Public Function CountPrimeFactors(ByVal n As Integer) As Integer
Dim count As Integer, f As Integer
If n = 1 Then
CountPrimeFactors = 0 GoTo Finish2
End If
If (IsPrime(n)) Then
CountPrimeFactors = 1 GoTo Finish2
End If
count = 0 f = 2
Do While (True)
If n Mod f = 0 Then
count = count + 1
n = n / f
If n = 1 Then
CountPrimeFactors = count
Exit Do
End If
If IsPrime(n) Then f = n
ElseIf f >= 3 Then
f = f + 2
Else
f = 3
End If
Loop
Finish2: End Function</lang>
Visual Basic .NET
<lang vbnet>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</lang>
- 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
Wren
<lang ecmascript>import "/fmt" for Fmt import "/math" for Int
var max = 120 System.print("The attractive numbers up to and including %(max) are:") var count = 0 for (i in 1..max) {
var n = Int.primeFactors(i).count
if (Int.isPrime(n)) {
System.write(Fmt.d(4, i))
count = count + 1
if (count%20 == 0) System.print()
}
} System.print()</lang>
- 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
zkl
Using GMP (GNU Multiple Precision Arithmetic Library, probabilistic primes) because it is easy and fast to test for primeness. <lang zkl>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");</lang>
Using Prime decomposition#zkl <lang 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;
}</lang>
- 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
(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
- Programming Tasks
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