Generate all factors of a number

allfactors.py

#!/usr/bin/env python3

''' Generate all factors of m

    Written by PM 2Ring 2016.10.20
'''

import sys
from itertools import product
from functools import reduce 
from operator import mul

def potential_primes():
    yield from (2, 3)
    n = 5
    while True:
        yield from (n, n+2)
        n += 6

def factorize(m):
    """ Put prime factors of m into a list of tuples (p, power) """
    seq = []
    for p in potential_primes():
        if p*p > m:
            seq.append((m, 1))
            break
        r = m % p
        if not r:
            k = 0
            while not r:
                m //= p
                k += 1
                r = m % p
            seq.append((p, k))
            if m == 1:
                break
    return seq

def allfactors(m):
    # Transpose the (p, power) list to get a tuple of prime factors 
    # and a tuple of the corresponding powers
    pr, pw = zip(*factorize(m))

    # iterate over all combinations of the valid powers for each prime
    result = [reduce(mul, (u**v for u, v in zip(pr, t))) 
        for t in product(*[range(v+1) for v in pw])]

    result.sort()
    return result

def main():
    m = int(sys.argv[1]) if len(sys.argv) > 1 else 120
    print(allfactors(m))

if __name__ == '__main__':
    main()