标题:
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
作者:
吴莉, 杨仕椿
关键字:
约数和函数, 正整数解, 标准分解式 Sum of Divisors; Positive Integer Solution; Standard Decomposition
期刊名称:
《Pure Mathematics》, Vol.3 No.2, 2013-03-12
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。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.