# Article

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Keywords:
arithmetic function; periodic function; homothetic function
Summary:
A homothetic arithmetic function of ratio $K$ is a function $f\colon \mathbb {N}\rightarrow R$ such that $f(Kn)=f(n)$ for every $n\in \mathbb {N}$. Periodic arithmetic funtions are always homothetic, while the converse is not 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 of the period and the ratio of $f$.
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