  Let $\phi(n)$ be the Euler totient function and $\sigma(n)$ denote the sum of
divisors of $n$. In this note, we obtain explicit upper bounds on the number of
positive integers $n\leq x$ such that $\phi(\sigma(n)) > cn$ for any $c>0$.
This is a refinement of a result of Alaoglu and Erd\H{o}s.
