An order result for the exponential divisor function
Abstract
Description
The integer $d=\prod_{i=1}^s p_i^{b_i}$ is called an exponential divisor of $n=\prod_{i=1}^s p_i^{a_i}>1$ if $b_i \mid a_i$ for every $i\in \{1,2,...,s\}$. Let $τ^{(e)}(n)$ denote the number of exponential divisors of $n$, where $τ^{(e)}(1)=1$ by convention. The aim of the present paper is to establish an asymptotic formula with remainder term for the $r$-th power of the function $τ^{(e)}$, where $r\ge 1$ is an integer. This improves an earlier result of {\sc M. V. Subbarao} [5].