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Mean value of an arithmetic function associated with the Piltz divisor function

Meselem Karras

Faculty of Science and Technology, Djilali Bounaama Khemis Miliana University, 44225, Algeria

Department of Mathematics, E.N.S., BP 92. Kouba 16016, Algiers, Algeria

E-mail Address: karras.m@hotmail.fr

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and

Abdallah Derbal

Faculty of Science and Technology, Djilali Bounaama Khemis Miliana University, 44225, Algeria

Department of Mathematics, E.N.S., BP 92. Kouba 16016, Algiers, Algeria

E-mail Address: abderbal@yahoo.fr

Corresponding author.

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https://doi.org/10.1142/S179355712050062XCited by:0 (Source: Crossref)

Abstract

Let $k$ $k$ be a fixed integer, we define the multiplicative function $D_{k} (n) = \frac{d_{k} (n)}{d_{k}^{*} (n)}$ $D_{k} (n) = \frac{d_{k} (n)}{d_{k}^{*} (n)}$ , where $d_{k} (n)$ $d_{k} (n)$ is the Piltz divisor function and $d_{k}^{*}$ $d_{k}^{*}$ is the unitary analogue function of $d_{k}$ $d_{k}$ . The main purpose of this paper to use elementary methods to study the mean value of the function $D_{k} (n)$ $D_{k} (n)$ .

Communicated by B. Diarra

Keywords:

AMSC: 11N37, 11A25

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