How would I find the inverse of $τ(n)=\sum_{d|n}1$ and $\sigma(n)=\sum_{d|n}d$ in terms of $\mu$? Where $µ$ is the Mobius function.
So I know $τ=u*u$ and $\sigma=N*u$ and also $u*\mu=I$ but I cant quite see how to get to the final steps.
I know I need to show that $τ^{-1}=\mu*\mu$ but can't quite see how to get to this step?
I think $\sigma^{-1}=N*\mu$ is that right?