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.

上界很明显为28123

1. 计算到上界为止所有数的和,记为sum,并将abundant数保存
2. 将abundant数两两相加,如不大于上界,则将这两数的和记为可以表示为abundant数相加,即不满足题意要求的数
3. 所有可表示为abundant数相加的数其和记为abundantsSum
4. 所求答案即为 sum - abundantsSum

4179871

Source:C++