Summary: Robin conjectured that \(\sigma(n) 7!\), where \(\sigma(n)\) is the sum of the divisors of \(n\) and \(\gamma\) denotes the Euler constant. Robin showed that the validity of this inequality is equivalent to the Riemann Hypothesis. Here we show that the set of \(n\)'s failing this inequality has a very small counting function: the number of such \(n \leq x\) is \(O(x^\varepsilon)\) for any \(\varepsilon > 0\) and \(x > x(\varepsilon)\).