Earlier today I thought I proved that the following series diverged:
$$\sum_{n=2}^\infty\frac{\phi(n)}{n^2}$$
as a result of a misapplication of the prime number theorem. I mistook $\phi(n)$ for $\pi(n)$ in the statement. Is this salvageable? I've been trying to find lower bounds for $\phi(n)$ that I may pass to, but the literature on this is a bit dense for me.
Thanks