Comptes Rendus
Théorie des nombres
On the denominators of harmonic numbers. IV
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 53-57.

Let be the set of all positive integers n such that the denominator of 1+1/2++1/n is less than the least common multiple of 1,2,,n. In this paper, under a certain assumption on linear independence, we prove that the set has the upper asymptotic density 1. The assumption follows from Schanuel’s conjecture.

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DOI : 10.5802/crmath.282
Classification : 11B05, 11B75
Mots clés : harmonic numbers, least common multiples, upper asymptotic density

Bing-Ling Wu 1 ; Xiao-Hui Yan 2

1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, P. R. China
2 School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, P. R. China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Bing-Ling Wu; Xiao-Hui Yan. On the denominators of harmonic numbers. IV. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 53-57. doi : 10.5802/crmath.282. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.282/

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[7] Bing-Ling Wu; Yong-Gao Chen On certain properties of harmonic numbers, J. Number Theory, Volume 175 (2017), pp. 66-86 | MR | Zbl

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[9] Bing-Ling Wu; Yong-Gao Chen On the denominators of harmonic numbers. II, J. Number Theory, Volume 200 (2019), pp. 397-406 | MR | Zbl

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