sum of all the amicable numbers under 10000

sum_amicable.py

from math import sqrt 

def _sum_of_proper_divisors(n, sum_of_proper_divisors):
	_sum = 1
	sqrt_n = int(sqrt(n))
	for i in range(2, sqrt_n+1):
		if n % i == 0:
			_sum += i
			if n // i != i:
				_sum += n // i

	sum_of_divsors_map[n] = _sum

def sum_of_proper_divisors(n, sum_of_proper_divisors):
	if n not in sum_of_divsors_map:
		_sum_of_proper_divisors(n, sum_of_proper_divisors)
	return sum_of_divsors_map[n]

def calculate_sum_of_amicable_numbers(upper_limit):
	_sum = 0
	sum_of_divsors_map = dict()
	for i in range(1, upper_limit + 1):
		sum_of_div = sum_of_proper_divisors(
			i, 
			sum_of_divsors_map
		)
		if (
			sum_of_div > i and 
			sum_of_div <= upper_limit and 
			sum_of_div != i and 
			sum_of_proper_divisors(sum_of_div, sum_of_divsors_map) == i
		):
				_sum += (sum_of_div + i)

	return _sum

if __name__ == '__main__':
	print(
		calculate_sum_of_amicable_numbers(10000)
	)