The Distribution of Values of Arithmetic Functions

Abstract

Let us usual $\tau _{k}(n)$ denote the number of ways $n$ may be written as a product of $k$ fixed factors. In this chapter there introduce the notation

$$ D_k(x) = \sum _{n \le x} \tau _k(n). $$

We show that the asymptotic formula for $D_k(x)$ is changing with growing values of $k$ and present specific values of $k$, which is a change.