Project Euler Question 23 Non-Abundant Numbers in Turkish

Project Euler Question 23 Non-Abundant Numbers in Turkish

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

If a number n has a sum of proper divisors less than n, it is called deficient, and if this sum exceeds n, it is called abundant.

Since 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, and the smallest number that can be written as the sum of two abundant numbers is 24. Through mathematical analysis, it can be shown that all integers greater than 28123 can be written as the sum of two abundant numbers. However, even though it is known that the largest number that cannot be expressed as the sum of two abundant numbers is below this limit, this upper bound cannot be reduced further.

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