On the integrality of the first and second elementary symmetricfunctions of $1, 1/2^{s_2}, ...,1/n^{s_n}$
It is well known that the harmonic sum $H_{n}(1)=\sum_{1\leq k\leq n}\frac{1}{k}$is never an integer for $n>1$. Erd\"{o}s and Niven proved in 1946 thatthe multiple harmonic sum$H_{n}(\{1\}^r)=\sum_{1\leq k_{1}<\cdots< k_{r}\leq n}\frac{1}{k_{1}\cdots k_{r}}$can take int...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2017-12-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | http://www.aimspress.com/article/10.3934/Math.2017.4.682/fulltext.html |