Define the function $G$ for integers $n>1$ by

where $\sigma(n)$ is the sum of the positive divisors of $n$.  A positive integer $N$ is said to be an extraordinary number if it is composite and

for any prime factor $p$ of $N$ and any multiple $aN$ of $N$.

It has been proved in [1] that the Riemann Hypothesis is true iff 4 is the only extraordinary number.  The proof is based on Gronwall’s theorem and Robin’s theorem.