Factorial, the funny way

import math
from collections import defaultdict
from copy import copy


def eratosthenes(n):
    sieve = set(range(2, n + 1))
    for p in range(2, int(math.sqrt(n)) + 1):
        if p in sieve:
            d = 2 * p
            while d <= n:
                try:
                    sieve.remove(d)
                except KeyError:
                    pass
                d += p
    return sieve


def get_prime_factor_freq(l, max, res, n=None, nfactors=None):
    n = 1 if n is None else n
    nfactors = defaultdict(int) if nfactors is None else nfactors

    r = copy(l)
    for e in l:
        r.remove(e)
        d = n
        dfactors = copy(nfactors)
        exp = 0

        d *= e
        while d <= max:
            dfactors[e] += 1
            exp += 1

            res[e] += exp
            for x, y in nfactors.items():
                res[x] += y

            get_prime_factor_freq(r, max, res, d, dfactors)
            d *= e


def factorial(n):
    a = eratosthenes(n)

    r = defaultdict(int)
    get_prime_factor_freq(a, n, r)

    res = 1
    for x, y in r.items():
        res *= x ** y
    return res


print(factorial(50))