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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 $k=3$

Topics:
Mathematics - Number Theory, 11J72

Year: 2011

DOI identifier: 10.1007/s11139-006-0154-3

OAI identifier:
oai:arXiv.org:1105.1452

Provided by:
arXiv.org e-Print Archive

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