  Let $G(n)=\sigma (n)/(n \log \log n )$. Robin made hypothesis that
$G(n)<e^\gamma$ for all integer $n>5040$. If there exists counterexample to
Robin hypothesis, then there must exist finite number of counterexamples
$n>5040$ such that $G(n)$ attains largest value. This article studies various
properties of such number.
