摘要
对任一正整数n,令σ(n)表示n的全部正因数的和函数,如果正整数n与正整数m满足σ(n)=σ(m)=n+m+1,那么称正整数对(n,m)为一对拟亲和数.讨论了正整数S_(n)=n^(2n)+1是否与其他的正整数构成拟亲和数的问题.基于初等的方法,证明了S_(n)不与任何正整数构成拟亲和数.
For any positive integern,letσ(n)denote the sum of all positive factors of n,if the positive integer n and the positive integer m satisfyσ(n)=σ(m)=n+m+1,then the positive integer pair(n,m)is said to be a pair of quasi-amicable number.The problem that whether the positive integer S_(n)=n^(2n)+1 and other positive integers constitute a quasi-amicable number was discussed.And by using elementary method,the conclusion that the positive integer S_(n)is not quasi-amicable number was proved.
作者
姜莲霞
张四保
Jiang Lianxia;Zhang Sibao(Kashi University;Research Center of Modern Mathematics and Its Application)
出处
《哈尔滨师范大学自然科学学报》
CAS
2023年第6期6-8,共3页
Natural Science Journal of Harbin Normal University
基金
国家自然科学基金项目(12061039)
新疆维吾尔自治区自然科学基金资助项目(2022D01A14)
关键词
亲和数
拟亲和数
初等方法
Number
Quasi-amicable number
Elementary method
