factors.py

#!/usr/bin/env python3
import functools
import itertools
import math


def prime_factors(n, sqrt=math.sqrt):
    limit = sqrt(n) + 1

    i = 2
    while i <= limit:
        entered = False

        while n % i == 0:
            entered = True
            n //= i
            yield i

        if entered:
            limit = 1 + sqrt(n)
        i += 1

    if n > 1:
        yield n


def all_factors(n,
                combinations=itertools.combinations,
                reduce=functools.reduce,
                mul=lambda x, y: x * y):
    yield 1

    ps = list(prime_factors(n))

    for i in range(1, len(ps) + 1):
        for ms in combinations(ps, i):
            yield reduce(mul, ms, 1)