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