A homothetic arithmetic function of ratio $K$ is a function $f \mathbb{N}\rightarrow R$ 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. https://www.rxkaitori.com/product-category/pls/