Euler #203

from math import factorial


def doubles(n):
    return len(set(n)) == len(n)


def factorize(n):
    factors = [1]
    while n % 2 == 0:
        factors.append(2)
        n = int(n/2)
    for b in range(3, int(n**0.5) + 1, 2):
        while n % b == 0:
            n = int(n/b)
            factors.append(b)
    if n > 2:
        factors.append(int(n))
    return doubles(factors)


def combination(n, k):
    return int(factorial(n)/(factorial(n-k)*factorial(k)))

nums = []
for x in range(51):
    for y in range(int(x/2) + 1):
        if combination(x, y) not in nums:
            nums.append(combination(x, y))

answer = 0
for i in nums:
    print(nums.index(i))
    if factorize(i):
        answer += i
print(answer)