Research article

On the Sum of Unitary Divisors Maximum Function

  • Received: 03 October 2016 Accepted: 10 December 2016 Published: 10 February 2017
  • It is well-known that a positive integer $d$ is called a unitary divisor of 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 $m\geq 1$.

    Citation: Bhabesh Das, Helen K. Saikia. On the Sum of Unitary Divisors Maximum Function[J]. AIMS Mathematics, 2017, 2(1): 96-101. doi: 10.3934/Math.2017.1.96

    Related Papers:

  • It is well-known that a positive integer $d$ is called a unitary divisor of 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 $m\geq 1$.


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  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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