#!/usr/bin/python3 # mari von steinkirch @2013 # steinkirch at gmail ''' 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_sum_proper_divisors(n): sum_proper_div = 0 for i in range(1, n): if n%i == 0: sum_proper_div += i return sum_proper_div def amicable_numbers(N): sum_div_list = [find_sum_proper_divisors(i) for i in range(1, N+1)] sum_amicable_numbers = 0 set_div = set() for a in range(1, N): da = sum_div_list[a-1] if da < N: b = da db = sum_div_list[b-1] if a != b and db == a and a not in set_div and b not in set_div: sum_amicable_numbers += a + b set_div.add(a) set_div.add(b) return sum_amicable_numbers def main(): print(amicable_numbers(10000)) print('Tests Passed!') if __name__ == '__main__': main()