On numbers satisfying Robin's inequality, properties of the next counterexample and improved specific bounds

Robert Vojak

Define $s(n):=n^{-1}\sigma (n)$ ($\sigma (n):={\sum }_{d|n}d)$ and $\omega (n)$ is the number of prime divisors of $n$. One of the properties of $s$ plays a central role: $s(p^a)>s(q^b)$ if $…