''' 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. '''

import math

def ami(x):
  test = 1
  sqr = int(math.ceil(math.sqrt(x)))
  if sqr * sqr == x: test += sqr
  for i in xrange(2, sqr + 1):
    if x % i == 0: test += i + x / i
  return test

for j in xrange(2, 10000):
  tmp = ami(j)
  if j == ami(tmp) and j != tmp:
    print j, '\t', tmp