# Gronwall’s theorem

The function

 $G(n)\;:=\;\frac{\sigma(n)}{n\ln(\ln{n})}\qquad(n\;=\;2,\,3,\,4,\,\ldots),$

in which $\sigma(n)$ means the sum of the positive divisors of $n$, satisfies the equation

 $\limsup_{n\to\infty}\,G(n)\;=\;e^{\gamma}$

where $\gamma$ is the Euler–Mascheroni constant.

## References

• 1 T. H. Gronwall:  Some asymptotic expressions in the theory of numbers.  $-$ Trans. Amer. Math. Soc. 14 (1913) 113–122.
Title Gronwall’s theorem GronwallsTheorem 2013-03-22 19:33:44 2013-03-22 19:33:44 pahio (2872) pahio (2872) 8 pahio (2872) Theorem msc 40A99 msc 11A25 msc 26A12 EulerMascheroniConstant RobinsTheorem