import os
import math
import numpy as np

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

# A number is abundant if its properdivisors sum to 
# more than the original number, e.g. 12 is abundant, since 12 can be divided
# by 1, 2, 3, 4, 6 = 16

# It can be proven that all numbers above 28123 can be written as the sum
# of 2 abundant numbers

def getDivisors(n):
	divs = [True] * math.ceil(n/2)

	for x in range(1, len(divs)):
		if divs[x] and n % (x + 1) != 0:
			y = x
			while y < len(divs):
				divs[y] = False
				y = y + x + 1

	res = []
	for x in range(len(divs)):
		if divs[x]:
			res.append(x + 1)
	return res

def isAbundant(n):
	return sum(getDivisors(n)) > n


def main():
	print("Hello, this is Patrick")

	m = 28123

	a = list(filter(isAbundant, range(1, m+1)))

	# We are assuming that the abundants are sorted
	sums = set([])
	for i in range(len(a)):
		for j in range(i, len(a)):
			s = a[i] + a[j]
			if s > m:
				break
			else:
				#print(s)
				sums.add(s)

	nonsums = set(range(1, m+1))
	nonsums.difference_update(sums)
	# print(nonsums)
	print(sum(nonsums))


if __name__ == "__main__":
	main()