$f$ is integrable but $Hf$ is not

My real analysis homework has the following question:

For $n\ge 3$ define $f=\sum_{n=3}^\infty \chi_{(n,n+{1\over n(\ln n)^2})}$. Show that $f$ is integrable but its associated Hardy Littlewood function $Hf$ is not.

I can easily show that $f$ is integrable. However, I have completely no idea how to prove $Hf$ is not, i.e. finding a lower estimate of $Hf$ such that this lower estimate diverges.