Lets recall the Möbius inversion formula:
If we have two arithmetic functions $f,F$, such:
$$F(n)=\sum_{d|n}f(d)$$ then we have:
$$f(n)=\sum_{d|n}F(d)\mu(\frac{n}{d})$$
Suppose now that we have another arithmetic functions $g , G$:
$$G(n,a,b)=\sum_{d|an+b}g(d)$$
Express g(n) in terms of $G(d,a,b)$, where $a,b$ are fixed.
I was trying to apply the proof of the Möbius inversion formula to solve this problem, but with no result.
Thank you in advance.