  Let $\{p_j(n)\}_{j=1}^{\omega(n)}$ denote the increasing sequence of distinct
prime factors of an integer $n$. We provide details for the proof of a
statement of Erd\H{o}s implying that, for any function $\xi(n)$ tending to
infinity with $n$, we have $$f(n):=\max_{1\leqslant j<\omega(n)}\log \Big({\log
p_{j+1}(n)\over \log p_j(n)}\Big)=\log_3n+O(\xi(n))$$ for almost all integers
$n$.
