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AIMS Mathematics

2017, Volume 2, Issue 1: 96-101. doi: 10.3934/Math.2017.1.96
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Research article

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: 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 $m\geq 1$.


    加载中
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    [2] David M. Burton, Elementary number theory, Tata McGraw-Hill Sixth Edition, 2007.
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    [4] P. Moree, H. Roskam, On an arithmetical function related to Euler’s totient and the discriminator. Fib. Quart., 33 (1995), 332-340.
    [5] J. Sandor, On certain generalizations of the Smarandnche function. Notes Num. Th. Discr. Math., 5 (1999), 41-51.
    [6] J. Sandor, A note on two arithmetic functions. Octogon Math. Mag., 8 (2000), 522-524.
    [7] J. Sandor, On a dual of the Pseudo-Smarandache function. Smarandnche Notition Journal, 13 (2002).
    [8] J. Sandor, A note on exponential divisors and related arithmetic functions. Sci. Magna, 1 (2005), 97-101.
    [9] J. Sandor, The unitary totient minimum and maximum functions. Sci. Studia Univ. ”Babes-Bolyai”, Mathematica, 2 (2005), 91-100.
    [10] J. Sandor, The product of divisors minimum and maximum function. Scientia Magna, 5 (2009), 13-18.
    [11] J. Sandor, On the Euler minimum and maximum functions. Notes Num. Th. Discr. Math., 15 (2009), 1-8.
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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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