For squarefree $i$ what is $\sum_i^{n} \frac{1}{i}$?

For squarefree $i$ what is $\sum_i^{n} \frac{1}{i}$?

For squarefree $i$ what is $\sum_i^{n} \frac{1}{i}$ ? I use $\sum_m \mu(m)
ln(\frac{n}{m^2}+\frac{1}{2})$. I know about the connection with
$\zeta(2)$ and $\frac{\zeta(s)}{\zeta(2s)}$ but that does not help ??
Can I do better ?