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AIMS Mathematics, 2017, 2(1): 96-101. doi: 10.3934/Math.2017.1.96. Research article

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On the Sum of Unitary Divisors Maximum Function

1 Department of Mathematics, B.P.Chaliha College, Assam-781127, India
2 Department of Mathematics, Gauhati University, Assam-781014, India

Received: , Accepted: , Published:

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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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Keywords: Unitary Divisor function; Smarandache function; Fermat prime

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

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Copyright Info: © 2017, Bhabesh Das, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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