On the distribution of the strongly multiplicative function $2^{\omega (n)}$ on the set of natural numbers

Abstract

In this paper, we study the distribution of the sequence of integers $2^{\omega (n)}$ under the assumption of the strong Riemann hypothesis, where $\omega (n)$ denotes the number of distinct prime divisors of $n$. We provide an asymptotic formula for the sum $\sum _{n\le x}{2}^{\omega (n)}$ under this assumption. We study the sum $\sum _{n\le x}{2}^{\omega (n)}$ unconditionally too.