The sum of reciprocals of least common multiples
type: Item
instance of: scholarly article
title: The sum of reciprocals of least common multiples
zbMATH Open document ID: 1499.11004
author: Jinhui Fang
author: Jie Ma
published in: Periodica Mathematica Hungarica
publication date: 2022-02-22T00:00:00Z
review text: Let \((a_i)_{i\ge 1}\) be a strictly increasing sequence of positive integers. In the paper under review, the authors consider the sums \[S:= \sum_{i=1}^n {\mathrm{lcm}} (a_i,\ldots, a_{i+r-1})^{-1}\] under the condition \({\mathrm{lcm}} (a_1, \ldots, a_{r-1}) \le a_r\), and determine the best upper bound for \(S\), depending uniformly only on \(r\) and \(n\). They also characterize the terms \(a_1,\ldots,a_{n+r-1}\) of the given sequence such that the best upper bound is attained. These results extend earlier related results by \textit{D. Borwein} [Can. Math. Bull. 21, 117--118 (1978; Zbl 0376.10003)] and \textit{G. Qian} [C. R., Math., Acad. Sci. Paris 355, No. 11, 1127--1132 (2017; Zbl 1401.11006)]. For Part II, see [\textit{J. Zhao} et al., Appl. Math. Comput. 399, Article ID 126003, 12 p. (2021; Zbl 07423476)].
reviewed by: László Tóth
Mathematics Subject Classification ID: 11A05
zbMATH DE Number: 7479504
zbMATH Keywords: least common multiple
zbMATH Keywords: sequences
zbMATH Keywords: upper bound
MaRDI profile type: Publication
full work available at URL: s10998-021-00395-w
OpenAlex ID: W3175277835
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cites work: Q4443440
DOI: 10.1007/S10998-021-00395-W
description: scientific article; zbMATH DE number 7479504