Let $f$ and $g$ be arithmetic functions. Recall that the Mobius inversion formula states:

$$ g(n)=\sum_{d|n}f(d) \ \Longleftrightarrow \ f(n)=\sum_{d|n}\mu(d)g\left(\frac nd \right) $$

...where $\mu(n)$ is the Mobius function defined by:

$$ \mu(n):=\begin{cases} (-1)^r &\mbox{ if }n=p_1p_2 \cdots p_r \mbox{ for distinct primes }p_1, \ldots, p_r \\\ 0 &\mbox{ otherwise.}\end{cases} $$

Which of the following statements are correct?

Select **ALL** that apply.