Examples of functions summables in $\mathbb{Z}^d$.

Question

I know that $f_0(x)={ 1 \over \vert \vert x\vert \vert^\alpha}$, $f_0(0)=1$ , $\alpha>d$, $d\in \mathbb{N}$ is summable in $\mathbb{Z}^d$, i.e.

$$ \sum_{x \in \mathbb{Z}^d} f(x)<\infty. $$ I am searching for other examples of $f(x)>{ 1 \over \vert \vert x\vert \vert^\alpha}$ (except maybe for a finite numbers of 'x's) that are summables in $\mathbb{Z}^d$ or $V_n= [1,n]^d \bigcap \mathbb{Z}^d$.