I feel like I've seen a formula somewhere for $\displaystyle \sum_{d|n} \frac {\mu(d)}d$, but I can't remember what it is and can't find it. Does anybody know of a formula?
2026-03-25 16:01:23.1774454483
Formula for $\sum_{d|n} \frac {\mu(d)}d$
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$$\sum_{d|n}\frac{\mu(d)}{d} = \prod_{p|n}(1-p^{-1}) = \frac{\varphi(n)}{n}$$ where $\varphi$ is Euler's function.