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arXiv · 1307.0083

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

Aleksandr Morkotun
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Abstract

We consider the function $G(n)=\frac{σ(n)}{n\log\log n}$ (where $σ(n)=\sum_{d|n}d$) 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.

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Aleksandr Morkotun. 2013-06-29. On the increase of Grönwall function value at the multiplication of its argument by a prime. https://arxiv.org/abs/1307.0083

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