Is there a way to simplify or reduce a double summation of of the form
$$\sum_{j=1}^n\sum_{i=1}^nf(n-ij)$$
where $f:\mathbb{Z}\rightarrow\mathbb{R}$ and $n$ is a positive integer?
It seems to me that I need an explicit formula that enumerates the set of ${ij}$ for a given $n$, but I could be wrong. Maybe summation by parts?
What's the best way to go about this?