  In this note, we study the arithmetic function $f : \mathbb{Z}_+^* \to
\mathbb{Q}_+^*$ 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.
