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arXiv · 2209.14573

Asymptotic formula for the multiplicative function $\frac{d(n)}{k^{ω(n)}}$

Meselem Karras
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Abstract

For a fixed integer $k$, we define the multiplicative function \[D_{k,ω}(n) := \frac{d(n)}{k^{ω(n)}}, \]where $d(n)$ is the divisor function and $ω(n)$ is the number of distinct prime divisors of $n$. The main purpose of this paper is the study of the mean value of the function $D_{k,ω}(n)$ by using elementary methods.

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Meselem Karras. 2022-10-14. Asymptotic formula for the multiplicative function $\frac{d(n)}{k^{ω(n)}}$. https://doi.org/10.46298/cm.10104

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