In a similar question to the one I last asked, there is another result I am struggling to understand. The proof I am studying also uses this line, where p is a prime and N $\in \mathbb{Z}$:
$1+\sum_{p|N}\frac{\log{p}}{p}=O(\log{(\log(3N)}))$
I am sure this result requires the use of Mertens' Theorems in some respect.
Many thanks in advance.