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...

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Bibliographic Details
Main Authors: Wanxi Yang, Mao Li, Yulu Feng, Xiao Jiang
Format: Article
Language:English
Published: AIMS Press 2017-12-01
Series:AIMS Mathematics
Subjects:
Online Access:http://www.aimspress.com/article/10.3934/Math.2017.4.682/fulltext.html

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