Divisors of a natural number

Divisors of a natural number is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Create a program to generate all the divisors of a given natural number.

Use it to generate and show here all the divisors of the numbers 2**(n-1) for n in the (inclusive) range [1, 16] and also for n = 31

Awk

<lang awk># Implemented by Arjun Sunel awk 'func divisors(n){printf "divisors of ";print n;printf " = [";for(j=1;j<n;j++){if(n%j==0){printf j;printf ","}};printf n;printf "]\n";}BEGIN{for(i=1;i<=16;i++)divisors((2^i) -1); divisors(2^31 -1)}' </lang>

Output:

divisors of 1 = [1]
divisors of 3 = [1,3]
divisors of 7 = [1,7]
divisors of 15 = [1,3,5,15]
divisors of 31 = [1,31]
divisors of 63 = [1,3,7,9,21,63]
divisors of 127 = [1,127]
divisors of 255 = [1,3,5,15,17,51,85,255]
divisors of 511 = [1,7,73,511]
divisors of 1023 = [1,3,11,31,33,93,341,1023]
divisors of 2047 = [1,23,89,2047]
divisors of 4095 = [1,3,5,7,9,13,15,21,35,39,45,63,65,91,105,117,195,273,315,455,585,819,1365,4095]
divisors of 8191 = [1,8191]
divisors of 16383 = [1,3,43,127,129,381,5461,16383]
divisors of 32767 = [1,7,31,151,217,1057,4681,32767]
divisors of 65535 = [1,3,5,15,17,51,85,255,257,771,1285,3855,4369,13107,21845,65535]

C

<lang c>// Implemented by Arjun Sunel

1. include<stdio.h>
2. include<math.h>

int divisors(int n) { int i, j; printf("divisors(%d) = [",n); for (i=1;i<n;i++) { if (n%i==0) printf("%d,",i);

} printf("%d]\n",i); }

int main() { int n,i;

for (i=1 ; i<=16;i++) { divisors(pow(2,i-1)); } divisors(pow(2,31-1)); return 0; }</lang>

Output:

divisors(1) = [1]
divisors(2) = [1,2]
divisors(4) = [1,2,4]
divisors(8) = [1,2,4,8]
divisors(16) = [1,2,4,8,16]
divisors(32) = [1,2,4,8,16,32]
divisors(64) = [1,2,4,8,16,32,64]
divisors(128) = [1,2,4,8,16,32,64,128]
divisors(256) = [1,2,4,8,16,32,64,128,256]
divisors(512) = [1,2,4,8,16,32,64,128,256,512]
divisors(1024) = [1,2,4,8,16,32,64,128,256,512,1024]
divisors(2048) = [1,2,4,8,16,32,64,128,256,512,1024,2048]
divisors(4096) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096]
divisors(8192) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192]
divisors(16384) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384]
divisors(32768) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768]
divisors(1073741824) = [1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,134217728,268435456,536870912,1073741824]

C++

<lang cpp>// Implemented by Arjun Sunel

1. include<iostream>
2. include<cmath>

using namespace std;

int divisors(int n) { int i, j; cout<<"divisors("<<n<<") = ["; for (i=1;i<n;i++) { if (n%i==0) cout <<i<<",";

} cout<<n<<"]"<<endl; }

int main() { int n,i;

for (i=1 ; i<=16;i++) { divisors(pow(2,i)-1); } divisors(pow(2,31)-1); return 0; } </lang>

Output:

divisors(1) = [1]
divisors(3) = [1,3]
divisors(7) = [1,7]
divisors(15) = [1,3,5,15]
divisors(31) = [1,31]
divisors(63) = [1,3,7,9,21,63]
divisors(127) = [1,127]
divisors(255) = [1,3,5,15,17,51,85,255]
divisors(511) = [1,7,73,511]
divisors(1023) = [1,3,11,31,33,93,341,1023]
divisors(2047) = [1,23,89,2047]
divisors(4095) = [1,3,5,7,9,13,15,21,35,39,45,63,65,91,105,117,195,273,315,455,585,819,1365,4095]
divisors(8191) = [1,8191]
divisors(16383) = [1,3,43,127,129,381,5461,16383]
divisors(32767) = [1,7,31,151,217,1057,4681,32767]
divisors(65535) = [1,3,5,15,17,51,85,255,257,771,1285,3855,4369,13107,21845,65535]
divisors(2147483647) = [1,2147483647]

Java

<lang java>// Implemented by Arjun Sunel

public class divisors { static void ans(double a) { System.out.print("divisors of " +(int)a + " = ["); for(int i = 1; i < a; i = i+1) { if (a%i==0) { System.out.print(i+","); } } System.out.print((int)a);

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

public static void main(String args[]) {

     	for(int x = 1; x <=16; x = x+1) 
     	{

ans(Math.pow(2,x)-1);

     	}
     	ans(Math.pow(2,31)-1);
  	}

} </lang>

Output:

divisors of 1 = [1]
divisors of 3 = [1,3]
divisors of 7 = [1,7]
divisors of 15 = [1,3,5,15]
divisors of 31 = [1,31]
divisors of 63 = [1,3,7,9,21,63]
divisors of 127 = [1,127]
divisors of 255 = [1,3,5,15,17,51,85,255]
divisors of 511 = [1,7,73,511]
divisors of 1023 = [1,3,11,31,33,93,341,1023]
divisors of 2047 = [1,23,89,2047]
divisors of 4095 = [1,3,5,7,9,13,15,21,35,39,45,63,65,91,105,117,195,273,315,455,585,819,1365,4095]
divisors of 8191 = [1,8191]
divisors of 16383 = [1,3,43,127,129,381,5461,16383]
divisors of 32767 = [1,7,31,151,217,1057,4681,32767]
divisors of 65535 = [1,3,5,15,17,51,85,255,257,771,1285,3855,4369,13107,21845,65535]
divisors of 2147483647 = [1,2147483647]

Python

<lang python>import math from operator import mul from itertools import product from functools import reduce

def fac(n):

   \
   return the prime factors for n
   >>> fac(600)
   [5, 5, 3, 2, 2, 2]
   >>> fac(1000)
   [5, 5, 5, 2, 2, 2]
   >>>  
   
   step = lambda x: 1 + x*4 - (x//2)*2
   maxq = int(math.floor(math.sqrt(n)))
   d = 1
   q = n % 2 == 0 and 2 or 3 
   while q <= maxq and n % q != 0:
       q = step(d)
       d += 1
   res = []
   if q <= maxq:
       res.extend(fac(n//q))
       res.extend(fac(q)) 
   else: res=[n]
   return res

def fact(n):

   \
   return the prime factors and their multiplicities for n
   >>> fact(600)
   [(2, 3), (3, 1), (5, 2)]
   >>> fact(1000)
   [(2, 3), (5, 3)]
   >>> 
   
   res = fac(n)
   return [(c, res.count(c)) for c in set(res)]

def divisors(n):

   factors = fact(n)   # [(primefactor, multiplicity), ...]
   primes, maxpowers = zip(*factors)
   powerranges = (range(m+1) for m in maxpowers)
   powers = product(*powerranges)
   return (
       reduce(mul,
              (prime**power for prime, power in zip(primes, powergroup)),
              1)
       for powergroup in powers)
   

if __name__ == '__main__':

   for n in list(range(1,17)) + [31]:
       tocalc = 2**n - 1
       print("divisors(%s) = %s" % (tocalc, sorted(divisors(tocalc))))</lang>

Output:

divisors(1) = [1, 1]
divisors(3) = [1, 3]
divisors(7) = [1, 7]
divisors(15) = [1, 3, 5, 15]
divisors(31) = [1, 31]
divisors(63) = [1, 3, 7, 9, 21, 63]
divisors(127) = [1, 127]
divisors(255) = [1, 3, 5, 15, 17, 51, 85, 255]
divisors(511) = [1, 7, 73, 511]
divisors(1023) = [1, 3, 11, 31, 33, 93, 341, 1023]
divisors(2047) = [1, 23, 89, 2047]
divisors(4095) = [1, 3, 5, 7, 9, 13, 15, 21, 35, 39, 45, 63, 65, 91, 105, 117, 195, 273, 315, 455, 585, 819, 1365, 4095]
divisors(8191) = [1, 8191]
divisors(16383) = [1, 3, 43, 127, 129, 381, 5461, 16383]
divisors(32767) = [1, 7, 31, 151, 217, 1057, 4681, 32767]
divisors(65535) = [1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535]
divisors(2147483647) = [1, 2147483647]