Mahler proved (a more general result that implies in particular) that \[2^k3^l<n^{1+o(1)}.\] Erdős [Er76d] wrote 'it is easy to see' that for infinitely many $n$ \[2^k3^l>n\log n.\] Steinerberger has noted a simple proof of this fact follows from taking $n=2^{3^r}$ for any integer $r\geq 1$, when $k=3^r$ and $l=r+1$.