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 $f mathbb{N}
ightarrow R$ such that $f(Kn)=f(n)$ for every $ninmathbb{N}$.Periodic arithmetic funtions are always homothetic, while the converse is trophy husband apron not true in general.In this paper we study homothetic and periodic exm1996 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 $f$.