"""
A perfect number is a number for which the sum of its proper 
divisors is exactly equal to the number. For example, the sum 
of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, 
which means that 28 is a perfect number.

A number n is called deficient if the sum of its proper divisors 
is less than n and it is called abundant if this sum exceeds n.

As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, 
the smallest number that can be written as the sum of two 
abundant numbers is 24. By mathematical analysis, it can be shown
that all integers greater than 28123 can be written as the sum of
two abundant numbers. However, this upper limit cannot be reduced
any further by analysis even though it is known that the greatest
number that cannot be expressed as the sum of two abundant 
numbers is less than this limit.

Find the sum of all the positive integers which cannot be written
as the sum of two abundant numbers.
"""
from Helper import properFactors

def isAbundant(n):
	factorsum = sum(properFactors(n))
	if factorsum > n:
		return True
	else:
		return False

nonAbundantSum = 0
for i in range(1, 28123):
	flag = False
	for j in range(int(i/2)+1):
		if isAbundant(j) == True and isAbundant(i-j) == True:
			flag = True
			break
	if flag == False:
		nonAbundantSum += i
print nonAbundantSum						
					