021.py

"""
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 util import *

dn_results = {}
amicable_sum = 0

for i in range(1, 10000):
    dn_results[i] = proper_divisor_sum(i)

for a in range(1, 10000):
    b = dn_results[a]
    if b in dn_results:
        if dn_results[b] == a and a != b:
            amicable_sum += a

print(amicable_sum)