文章目錄

原题链接 http://projecteuler.net/problem=23

Non-abundant sums

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.

非盈数之和

如果一个数的所有真因子之和等于数本身,则这个数被称为完美数。例如,28的所有真因子之和为1 + 2 + 4 + 7 + 14 = 28,这也就是说28是一个完美数。

一个数的所有真因子之和如果小于这个数则这个数称为亏数,如果大于这个数,则这个数称为盈数。

12是最小的盈数,因为1 + 2 + 3 + 4 + 6 = 16。能够被写成两个盈数之和的数是24.通过数学分析,可以知道,大于28123的所有整数都可以写成两个盈数之和。然而,通过分析,无法推断出这个上限,即使已经知道不能被表示成两个盈数之和的数中最大的数不会超过这个限制。

求所有不能被表示成两个盈数之和的正整数之和。

这题没什么好说的,直接算就是了。

打赏作者

文章目錄