How to relate $\sum_{n=0}^k a_nf(n)$ where $f:\mathbb{N}\to\mathbb{N}$ is a bijection to the sum $\sum_{n=0}^k a_nn$?

Question

suppose you're give these two sums: $\sum_{n=0}^k a_nf(n)$ where $f:\mathbb{N}\to\mathbb{N}$ is a bijection and $\sum_{n=0}^k a_nn$. is it possible to relate them in any way?