HMMT 2007 T3

Prove that for every integer $n$ greater than 1 ,

$\sigma(n) \phi(n) \leq n^{2}-1$

When does equality hold?

Dataset text NuminaMath olympiads. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.