  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.
