Let be the n-th harmonic number and let be its denominator. It is well known that is even for every integer . In this paper, we study the properties of . One of our results is: the set of positive integers n such that is divisible by the least common multiple of has density one. In particular, for any positive integer m, the set of positive integers n such that is divisible by m has density one.
Soit le n-ième nombre harmonique et notons son dénominateur. Il est bien connu que est pair pour tout entier . Dans ce texte, nous étudions les propriétés de . Un de nos résultats montre que l'ensemble des entiers positifs n tels que soit divisible par le plus petit commun multiple de est de densité 1. En particulier, pour tout entier positif m, l'ensemble des entiers positifs n tels que soit divisible par m est de densité 1.
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Bing-Ling Wu 1; Yong-Gao Chen 1
@article{CRMATH_2018__356_2_129_0, author = {Bing-Ling Wu and Yong-Gao Chen}, title = {On the denominators of harmonic numbers}, journal = {Comptes Rendus. Math\'ematique}, pages = {129--132}, publisher = {Elsevier}, volume = {356}, number = {2}, year = {2018}, doi = {10.1016/j.crma.2018.01.005}, language = {en}, }
Bing-Ling Wu; Yong-Gao Chen. On the denominators of harmonic numbers. Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 129-132. doi : 10.1016/j.crma.2018.01.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.01.005/
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☆ This work was supported by the National Natural Science Foundation of China (No. 11771211) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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