sum of all the positive integers which cannot be written as the sum of two abundant numbers.

sum_of_2_non_abundant.py

from math import sqrt


def sum_of_divisors(number):
	_sum = 1
	nsqrt = int(sqrt(number))
	for i in range(2, nsqrt + 1):
		if number % i == 0:
			_sum += i 
			if (number / i != nsqrt):
				_sum += number // i
	return _sum


def is_abundant(number):
	_sum_div = sum_of_divisors(number)
	if _sum_div > number:
		return True
	else:
		return False


upper_limit = 28123 + 100
tracker = [False] * (upper_limit + 1)
tracker[12] = True
abundant_numbers = [12]
_sum = sum(range(1, 13))
for num in range(13, upper_limit + 1):
	if is_abundant(num):
		tracker[num] = True
		abundant_numbers.append(num)
	for i in abundant_numbers:
		if tracker[num - i]:
			break
	else:
		_sum += num
print(_sum)