The irrationality of a number theoretical series

Details The irrationality of a number theoretical series The irrationality of a number theoretical series

2011-05-07

arxiv.org/abs/1105.1452v1

Ramanujan J. 12 (2006), no. 3, 455--460

Mathematics

Number Theory

Scientific paper

10.1007/s11139-006-0154-3

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 $k=3$.

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