Robin's inequality for 20-free integers

Abstract

In 1984, Robin showed that the Riemann Hypothesis for $\zeta$ is equivalent to demonstrating $\sigma (n)<e^{\gamma }n\log \log n$ for all $n>5040$. Robin's inequality has since been proven for various infinite families of power-free integers: $5$-free integers, $7$-free integers, and $11$-free integers. We extend these results to cover $20$-free integers.