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The irrationality of a number theoretical series

By Jan-Christoph Schlage-Puchta


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
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