Determine $f(n)$ such that for all $n\geq 1$,
$$\frac{1}{\varphi (n)}=\sum_{d\vert n}\left(\frac{1}{d}\right)f\left(\frac{n}{d}\right)$$
This is not a homework question, just a question I stumbled upon.
I have tried writing $\varphi (n)$ as
$$\varphi (n)=\sum_{d\vert n}^{}{\mu(d) \frac{n}{d}},$$ where $\mu$ is the Möbius function.
I am not sure if this is the right approach, but I was stuck here.
Sincere thanks for any help!