It is well-known that the Mertens function $M(n)=\sum_{k=1}^n\mu(k)$ changes sign infinitely many times when $n\rightarrow +\infty$. Let $f(n)=\sum_{k=1}^n\frac{\mu(k)}{k}$, then $\lim_{n\rightarrow +\infty}f(n)= 0$.

Question: Is the function $f(n)=\sum_{k=1}^n\frac{\mu(k)}{k}$ also changes sign infinitely many times when $n\rightarrow +\infty$ ?

It is well-known that the Mertens function $M(n)=\sum_{k=1}^n\mu(k)$ changes sign infinitely many times when $n\rightarrow +\infty$. Let $f(n)=\sum_{k=1}^n\frac{\mu(k)}{k}$, then $\lim\limits_{n\rightarrow +\infty}f(n)= 0$.

Question: Does the function $f(n)=\sum_{k=1}^n\frac{\mu(k)}{k}$ also change sign infinitely many times when $n\rightarrow +\infty$ ?