A study of a curious arithmetic function

Abstract

In this note, we study the arithmetic function $f:{\mathbb{Z}}_{+}^{\ast }\to {\mathbb{Q}}_{+}^{\ast }$ defined by $f(2^k\ell )={\ell }^{1-k}$ ($\forall k,\ell \in \mathbb{N}$, $\ell$ odd). We show several important properties about that function and then we use them to obtain some curious results involving the 2-adic valuation.

arXiv commentTo appear