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.

defsum_proper_factors(n): (result, sqrt) = (1, n ** 0.5)

(start, step) = n % 2 == 1and (3, 2) or (2, 1) for i in range(start, int(sqrt) + 1, step): if n % i == 0: result += i + n / i

if sqrt == int(sqrt): result -= sqrt

return result

defmain(): result = 0 for i in range(1, 10000): sum1 = sum_proper_factors(i) if sum1 > i: if i == sum_proper_factors(sum1): result += i + sum1 print result

if __name__ == '__main__': import time startTime = time.time() main() print time.time() - startTime