Find an example of a non-negative sequence $\displaystyle \{a_n\}$ such that $\displaystyle \textstyle \sum a_n^2$ converges but $\displaystyle \textstyle \sum \frac {a_n} n$ diverges.

I only know what it cannot be. It cannot be $\displaystyle \frac 1 {n^s}$ for any real s, it cannot be $\displaystyle \frac 1 {log^s n}$ for any real s, and obviously any geometric series won't work...

I'm stuck. I would appreciate a hint.