On a certain class of arithmetic functions

On a certain class of arithmetic functions

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A homothetic arithmetic function of ratio $K$ is a function $f hard steel shot mathbb{N} ightarrow R$ such that $f(Kn)=f(n)$ for every $ninmathbb{N}$.Periodic arithmetic funtions are always homothetic, while the converse is not true in general.In this paper we nova upright walker study homothetic and periodic arithmetic functions.

In particular we give an upper bound for the number of elements of $f(mathbb{N})$ in terms of the period and the ratio of $f$.