p21.py

"""
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.
"""

def sum_of_divisors(n):
    sum = 0
    for i in range(1, n):
        if n % i == 0:
            sum += i
    return sum

def is_amicable(a, b):
    return sum_of_divisors(a) == b and sum_of_divisors(b) == a

def sum_of_amicable_numbers(n):
    sum = 0
    for i in range(1, n):
        if is_amicable(i, sum_of_divisors(i)):
            if i != sum_of_divisors(i):
                sum += i
    return sum

print(sum_of_amicable_numbers(10000))