Geodesic
Théorie des nombres
On the denominators of harmonic numbers. IV
Wu, Bing-Ling1 ; Yan, Xiao-Hui2 
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
Comptes Rendus. Mathématique, Tome 360 (2022) no. G1, pp. 53-57.

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Let ℒ 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 ℒ 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
Keywords: harmonic numbers, least common multiples, upper asymptotic density

Wu, Bing-Ling 1 ; Yan, Xiao-Hui 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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Wu, Bing-Ling; Yan, Xiao-Hui. On the denominators of harmonic numbers. IV. Comptes Rendus. Mathématique, Tome 360 (2022) no. G1, pp. 53-57. doi : 10.5802/crmath.282. http://geodesic.mathdoc.fr/articles/10.5802/crmath.282/

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