p021.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.

import euler

def compute(n):
    ans = 0
    for i in range (1,n):
        d_n = sum(euler.divisors(i)) + 1
        d_m = sum(euler.divisors(d_n)) + 1
        if d_n != d_m and d_m == i:
            # Aufpassen Zahlen werden doppelt gezaehlt, wenn man direkt beide addiert
            ans = ans + d_n
    return ans

if __name__ == "__main__":
    print(compute(10000))