Meselem Karras - Asymptotic formula for the multiplicative function $\frac{d(n)}{k^{\omega(n)}}$

cm:10104 - Communications in Mathematics, October 18, 2022, Volume 31 (2023), Issue 1 - https://doi.org/10.46298/cm.10104
Asymptotic formula for the multiplicative function $\frac{d(n)}{k^{\omega(n)}}$

Authors: Meselem Karras

    For a fixed integer $k$, we define the multiplicative function \[D_{k,\omega}(n) := \frac{d(n)}{k^{\omega(n)}}, \]where $d(n)$ is the divisor function and $\omega (n)$ 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 $D_{k,\omega}(n)$ by using elementary methods.


    Volume: Volume 31 (2023), Issue 1
    Published on: October 18, 2022
    Accepted on: October 4, 2022
    Submitted on: September 30, 2022
    Keywords: Mathematics - Number Theory

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