On the increase of Grönwall function value at the multiplication of its argument by a prime

Abstract

We consider the function $G(n)=\frac{\sigma (n)}{n\log \log n}$ (where $\sigma (n)={\sum }_{d|n}d$) and set an imposed condition on its argument $n$, the fulfillment of which is sufficient for the existence of a prime $p$, at which $G(np)>G(n)$. This inequality is of interest in connection with the Robin's inequality. The paper also presents the results of numerical experiment conducted with superabundant numbers.

6 pages, 1 table

References in corpus (1)

• Superabundant numbers, their subsequences and the Riemann hypothesis