A study of a curious arithmetic function

Details A study of a curious arithmetic function A study of a curious arithmetic function

2010-04-13

arxiv.org/abs/1004.2269v1

Mathematics

Number Theory

To appear

Scientific paper

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.

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