# Double sum – Miklos Schweitzer 2010

There is a question in the Miklos Schweitzer contest last year that keeps bugging me. Here it is:

Is there any sequence $(a_n)$ of nonnegative numbers for which $\displaystyle\sum_{n \geq 1}a_n^2 <\infty$ and $$\sum_{n \geq 1}\left(\sum_{k \geq 1}\frac{a_{kn}}{k}\right)^2=\infty\quad?$$