# -.- coding: latin-1 -.- from math import sqrt """ 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. """ try: xrange # Python 2 except NameError: xrange = range # Python 3 def sum_of_divisors(n): total = 0 for i in xrange(1, int(sqrt(n) + 1)): if n % i == 0 and i != sqrt(n): total += i + n // i elif i == sqrt(n): total += i return total - n def solution(n): """Returns the sum of all the amicable numbers under n. >>> solution(10000) 31626 >>> solution(5000) 8442 >>> solution(1000) 504 >>> solution(100) 0 >>> solution(50) 0 """ total = sum( [ i for i in range(1, n) if sum_of_divisors(sum_of_divisors(i)) == i and sum_of_divisors(i) != i ] ) return total if __name__ == "__main__": print(solution(int(str(input()).strip())))