from e007 import is_prime
from e012 import factor

MIN = 2
MAX = 10000

def proper_divisors(n):
    """Returns the proper divisors of n
    
    Proper divisors are defined as numbers less than n which divide evenly into n
    """
    divisors = factor(n)
    # Knock off the last factor, since it is equal to n
    return divisors[:-1]

sums = {}
amicable = []
i = MIN
while i < MAX:
    if not is_prime(i):
        s = sum(proper_divisors(i))
        sums[i] = s
        if s in sums and i == sums[s] and i != s:
            print i, s, sums[s]
            amicable.append(i)
            amicable.append(s)
    i = i + 1
print 'Sum of amicable numbers less than {0}: {1}'.format(MAX, sum(amicable))