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Let $M(x) = \sum_{n\leq x} \mu(n)$ and $m(x) = \sum_{n\leq x} \frac{\mu(n)}{n}$, where $\mu(n)$ is the Möbius function. We know that (it is not the best known bounds): $$\limsup_{x \to \infty} M(x)x^{-...