%0 Journal Article
%T The irrationality of a number theoretical series
%A Jan-Christoph Schlage-Puchta
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/s11139-006-0154-3
%X Denote by $\sigma_k(n)$ the sum of the $k$-th powers of the divisors of $n$, and let $S_k=\sum_{n\geq 1}\frac{\sigma_k(n)}{n!}$. We prove that Schinzel's conjecture H implies that $S_k$ is irrational, and give an unconditional proof for the case $k=3$.
%U http://arxiv.org/abs/1105.1452v1