  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.
