Exercise 4.3.3 ($\sum_{j = 1}^\infty \mu(j!)$)

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Evaluate $\sum_{j = 1}^\infty \mu(j!)$.

Richard Ganaye · Accepted Answer

\begin{proof} 
If $j\geq 4$, then $4 \mid j!$, thus $j!$ is not square-free, so $\mu(j!) = 0$. This shows that
$$\sum_{j = 1}^\infty \mu(j!) = \mu(1) + \mu(2) + \mu(6) = 1 - 1 + 1 = 1.$$

\end{proof}

Exercise 4.3.3 ($\sum_{j = 1}^\infty \mu(j!)$)

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Exercise 4.3.3 ($\sum_{j = 1}^\infty \mu(j!)$)

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