\begin{equation} \sigma(n) < e^\gamma n \log \log n \end{equation}

In 1984 Guy Robin proved that the inequality is true for all n ≥ 5,041 if and only if the Riemann hypothesis is true (Robin 1984).

I could not get a hold of his paper. I am trying to understand how did he derived the inequality. Can anyone can outline the steps, how Robin derived this criterion?