Project Euler 第23题

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.

perfect number ：完美数，真因数的和等于其本身，如6=1+2+3

abundant number：过剩数，真因数和大于其本身，如12<1+2+3+4+6

deficient number：亏数，真因数和小于其本身，如4>1,2

当大于某个上界后，任何一个整数都等于为两个过剩数的和。找出不能被表示为两个过剩数的和的数的和。