Euler – Coder.si

Amicable numbers

Problem 21

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 tools import divisors


def run(limit=10000):
    tmp = {}
    result = 0
    for x in range(1, limit):
        if x in tmp:
            dx = tmp[x]
        else:
            dx = sum(list(divisors(x))) - x
            tmp[x] = dx
        if x != dx:
            if dx in tmp:
                dy = tmp[dx]
            else:
                dy = sum(list(divisors(dx))) - dx
                tmp[dx] = dy
            if dy == x:
                result += dx
    return result