与约数和函数σ（n）有关的一些不等式的解
The Solutions of Some Inequalities of the Sum of Distinct Divisors Function
DOI: 10.12677/PM.2013.32017, PDF,    科研立项经费支持
作者: 吴 莉*, 杨仕椿：阿坝师范高等专科学校数学系
关键词: 约数和函数；正整数解；标准分解式； Sum of Divisors; Positive Integer Solution; Standard Decomposition
摘要: 约数和函数是一类基本而又重要的数论函数。本文推广了由Bencze提出的两个公开问题的结论，证明了对于任意给定的正整数k和非零整数b，均存在无穷多个正整数n，使得以下三个不等式同时成立：，，，其中为任意正整数n的不同约数之和。
Abstract: The sum of distinct divisors is a basic and important arithmetical function. In this paper, we extend the conclusions of two open problems proposed by Bencze and prove that, for any given positive integers k and non-zero integers b, there exists infinitely many positive integers n such that the following three inequalities hold simultaneously: , and , where denotes the sum of distinct divisors of n.
文章引用：吴莉, 杨仕椿. 与约数和函数σ（n）有关的一些不等式的解[J]. 理论数学, 2013, 3(2): 107-111. http://dx.doi.org/10.12677/PM.2013.32017

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