problem_21.py

import collections


CACHE = collections.defaultdict(set)
CACHE[1].add(1)


def divisors(n):

    if not CACHE[n]:
        d = n

        while d >= 1:
            n % d or CACHE[d] and CACHE[n].update(CACHE[d]) or CACHE[n].add(d)
            d -= 1

    result = CACHE[n].copy()

    if len(result) > 1:
        result.remove(n)

    return result


def divisors_sum(n):
    return sum(divisors(n))


def main():

    numbers = []
    n = 1

    while n < int(1e4):

        number = divisors_sum(n)

        if number != n and  n == divisors_sum(number):
            numbers.append(n)

        n += 1

    return sum(numbers)


if __name__ == '__main__':
    result = main()
    print(result)