Article ID: MTJPAM-D-24-00089

Title: A study of restricted divisor functions with coprime conditions


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00089; Volume 6 / Issue 3 / Year 2024, Pages 284-298

Document Type: Research Paper

Author(s): ‪Nazli Yildiz Ikikardes a , Daeyeoul Kim b

aDepartment of Mathematics and Science Education, Necatibey Faculty of Education, Balikesir University, Turkey

bDepartment of Mathematics and Institute of Pure and Applied Mathematics, Jeonbuk National University, Korea

Received: 24 June 2024, Accepted: 8 July 2024, Published: 9 September 2024

Corresponding Author: Daeyeoul Kim (Email address: kdaeyeoul@jbnu.ac.kr)

Full Text: PDF

Abstract

For a natural number N, let E(N):=\sum\limits_{{d|N}\atop{d\equiv 1} \pmod 3} 1 - \sum\limits_{{d|N}\atop{d \equiv -1 \pmod 3}}1 and \lambda(N) := E(N) - 3 E\left(\frac{N}{3}\right). The formula for convolution sums \sum\limits_{t=1}^{N-1} \lambda(t)\lambda(N-t) is very well known. In this article, \sum\limits_{t=1\atop \gcd (t,N-t)=1}^{N-1} \lambda (t) \lambda(N-t) is calculated using arithmetical inverse of \lambda defined by Dirichlet convolution. Furthermore, we define the homogeneous Dirichlet convolution sum of arithmetical functions and find formulas of the homogeneous Dirichlet convolution sums of the inverse divisor functions.

Keywords: Dirichlet convolution, homogeneous convolution sums, restricted divisor functions

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Cite this article

How to cite this article: N. Y. Ikikardes and D. Kim, A study of restricted divisor functions with coprime conditions, Montes Taurus J. Pure Appl. Math. 6 (3), 284-298, 2024; Article ID: MTJPAM-D-24-00089.