"""
Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.
"""


def find_divisors(n):
    result = set()
    result.add(1)
    for i in range(2, int(n ** 0.5) + 1):
        if not n % i:
            if i <= n // i:
                result.add(i)
                result.add(n // i)
    return result


if __name__ == '__main__':
    amicable = []
    for a in range(2, 10000):
        if a in amicable:
            continue
        b = sum(find_divisors(a))
        if b == 1 or a == b:
            continue
        if sum(find_divisors(b)) == a:
            amicable.append(a)
            amicable.append(b)

    print(sum(amicable))
