On a certain class of arithmetic functions
Mathematica Bohemica, Tome 142 (2017) no. 1, pp. 21-25.

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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 $f$.
DOI : 10.21136/MB.2017.0071-14
Classification : 11A25, 11B99, 11N37
Mots-clés : arithmetic function; periodic function; homothetic function 
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Oller-Marcén, Antonio M. On a certain class of arithmetic functions. Mathematica Bohemica, Tome 142 (2017) no. 1, pp. 21-25. doi : 10.21136/MB.2017.0071-14. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2017.0071-14/

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