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. 

from funcs import is_prime

def divisors(n):
    # return proper divisors of n
    L = [1]
    
    for i in range(2, n//2+2):
        if n % i == 0:
            L.append(i)

    return L

amicable = {}
# pretty slow but it works
for i in range(1, 10001):
    if i not in amicable and not is_prime(i):
        check = sum(divisors(i))
        #print(f"{i}: {sum(divisors(i))}")

        if not is_prime(check) and check != i:
            if sum(divisors(check)) == i:
                amicable.update({i:check})
                amicable.update({check:i})

print(amicable)
print(sum(amicable))
Click to reveal output 
{220: 284, 284: 220, 1184: 1210, 1210: 1184, 2620: 2924, 2924: 2620, 5020: 5564, 5564: 5020, 6232: 6368, 6368: 6232}
31626

See problem 21 on projecteuler.net