21_AmicableNumbers.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 divisors(n):
    items = []
    for i in range(1, n // 2 + 1):
        if n % i == 0:
            items.append(i)
    return items


def d(n):
    return sum(divisors(n))


total = 0
for n in range(1, 10000):
    if n == d(d(n)) and n != d(n):
        total = total + n
print(total)