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 not blue banana gorra true in general.In this paper we study homothetic and periodic arithmetic functions.In particular we give an upper bound for the number of elements of $f(mathbb{N})$ in terms esp ltd sd-2 of the period and the ratio of $f$.