Hello.

If $\displaystyle f$ is multliplicative and $\displaystyle n=\prod_{i=1}^k{p_i^{n_i}}$, show that:

$\displaystyle \sum_{d|n}f(d)=\prod_{i=1}^k(1+f(p_i)+f(p_i^2)+... +f(p_i^{n_i})$

Thanks so much.