021.py

"""
    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.
    
    
    Answer: 51e04cd4e55e7e415bf24de9e1b0f3ff
"""
from common import check, get_factors

PROBLEM_NUMBER = 21
ANSWER_HASH = "51e04cd4e55e7e415bf24de9e1b0f3ff"
TOTAL_NUMBER = 10000

totals = {}
result = set()
for i in range(1, TOTAL_NUMBER):
    if i in result:
        continue
    factors = get_factors(i)
    sub_total = sum(factors) - i
    totals[i] = sub_total

    if sub_total != i and sub_total in totals and totals[sub_total] == i:
        result.add(i)
        result.add(sub_total)
        print(i, sub_total)

total = sum(result)
check(total, PROBLEM_NUMBER, ANSWER_HASH)