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In A cell complex in number theory by Anders Björner, 2011 a number theoretic cell complex is described which has the property that the Euler characteristic is related to the Mertens function: $$M(n) =...

Cross-posted from MathStackExchange, where the question is bountied but has not received any comment or answer) Some months ago, I derived the following formula for the Merten's function $M(n)$ using ...

Let $\Phi(x,p)$ = the number of integers $i$ where $0 < i \le x$ and $\gcd(x,p)=1$. Let $p\#$ be the primorial for $p$. Using the inclusion-exclusion principle: $$\Phi(x,p\#) = \sum_{d|p\#}\mu(d)...

My question is on Mobius inversion formula convergence/properties when used with infinite sums of function. Lets consider (on $\mathbb{R}^{+}$): $$S(x)= \sum\limits_{n=1}^{\infty} f(nx)$$ We call $...