There is Mertens function: $$M(x)=\sum_{n \le x}\mu(n)$$
How to calculate time of computing value of $M(N)$ for particular $N$?
I would like for example find that time using this formula: $$M(x)=1-\sum_{d\ge2}M(\frac{x}{d})$$
If we suppose that time to compute $M(x)$ is $O(f(x))$ then we get $f(x)=f(\frac{x}{2})+f(\frac{x}{3})+...$ And we need to find formula for $f$
Neverthelss i think i have done something wrong.
I hope for help.