On the Sum of Unitary Divisors Maximum Function

AIMS Mathematics

关键词: : ;    Unitary Divisor function;    Smarandache function;    Fermat prime;   

DOI  :  10.3934/Math.2017.1.96

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

It is well-known that a positive integer $d$is called a unitary divisorof an integer $n$ if $d|n$ and gcd$\left(d,\frac{n}{d}\right)=1$. Divisor function $\sigma^{*}(n)$denote the sum of all such unitary divisors of $n$.In this paper we consider the maximum function $U^{*}(n)=\max\{k\in\mathbb{N}:\sigma^{*}(k)|n\}$and study the function $U^{*}(n)$ for $n=p^{m}$,where$p$ is a prime and $m\geq 1$.

【 授权许可】

CC BY