Arithmetic properties of the Genocchi numbers and their generalization

This note is devoted to establish some new arithmetic properties of the generalized Genocchi numbers $G_{n,a}$ ($n\in \mathbb{N}$, $a\ge 2$). The resulting properties for the usual Genocchi numbers $G_n=G_{n,2}$ are then derived. We show for example that for any even positive integer $n$, the Genocchi number $G_n$ is a multiple of the odd part of $n$.