Question 2
(BEL 1) Let $n$ be a positive integer. Let $\sigma(n)$ be the sum of the natural divisors $d$ of $n$ (including $1$ and $n$). We say that an integer $m\ge1$ is superabundant (P. Erdős, 1944) if $\forall k\in\{1,2,\ldots,m-1\},\ \frac{\sigma(m)}m>\frac{\sigma(k)}k$. Prove that there exists an infinity of superabundant numbers.