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.
i have been trying to debug this code ever since i wrote it. all i managed to do is speed it up
that is a good thing but getting wrong answer is not. i added a HashSet to eliminate duplicates and it gave a smaller answer, but still much greater than correct answer. i changed the limit to 30000 and i am getting 29999 as a number that cannot be written as the sum of two abundant numbers. so i am definately doing something wrong but i can't see it. my ArrayList of abundant numbers looks ok, as does the listing of all the positive integers which cannot be written as the sum of two abundant numbers(24 is missing as is 30 etc.