Nonzero element in ${\rm Hom}_\mathbb{Z}(\prod_{n\geq 2}\mathbb{Z}/n\mathbb{Z},\mathbb{Q})$

Question

I want to check whether there is a nonzero element in ${\rm Hom}_\mathbb{Z}(\prod_{n\geq 2}\mathbb{Z}/n\mathbb{Z},\mathbb{Q})$. If exists, how to construct such element?