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$\begingroup$ The formula for $\Lambda(n)$ in your 2014 edit is incorrect when $n=1$. For $n>1$ the formula is a disguised version of the formula $\Lambda(n) = -\sum_{d|n} \mu(d)\log d$, which is true for all $n$, including $n=1$, and comes from equating Dirichlet series coefficients on both sides of $-\zeta’(s)/\zeta(s) = (1/\zeta(s))(\zeta’(s))$ for ${\rm Re}(s) > 1$. $\endgroup$

KConrad
– KConrad

2022-01-30 13:37:06 +00:00
Commented Jan 30, 2022 at 13:37

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