#-.- coding: latin-1 -.-
from __future__ import print_function
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
sums = []
total = 0
for i in xrange(1, 10000):
n = sum_of_divisors(i)
if n < len(sums):
if sums[n-1] == i:
total += n + i
sums.append(n)
print(total)