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The Möbius function $\mu (n)$ can be computed using $$\mu (n)=\sum_{\stackrel{1\le k \le n }{ \gcd(k,\,n)=1}} e^{2\pi i \frac{k}{n}}$$ (from An Introduction to the Theory of Numbers by Hardy and Wright). Maybe there is a fromula for the Möbius function which does not use the notion of divisibility. Can the Möbius function be interpolated by some analytic function?

Poder Rac
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    Not from this formula I'd say. There is one with some interesting arithmetical/analytical meaning. Note that every sequence can be interpolated by many entire functions ($\sin(\pi x)$ vanishes at the integers and $\sin(\pi x)/x$ is non-zero only once) – reuns Apr 07 '20 at 22:46
  • Actually the formula you provided is sufficient for me. – Poder Rac Apr 07 '20 at 23:39

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