Are the hyperharmonics integral? A partial answer via the small intervals containing primes

Rachid Aït Amrane; Hacène Belbachir

doi:10.1016/j.crma.2010.12.015

Combinatorics/Algebra

Are the hyperharmonics integral? A partial answer via the small intervals containing primes

Presented by: the Editorial Board

Rachid Aït Amrane ¹; Hacène Belbachir ²

¹ESI/École nationale supérieure d'informatique, BP 68M, Oued Smar, 16309, El Harrach, Alger, Algeria
²USTHB, faculté de mathématiques, BP 32, El Alia, 16111 Bab Ezzouar, Alger, Algeria

Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 115-117

Abstract (Original language)
Résumé

In a recent work, the authors have used Bertrand's postulate to give a partial answer to the conjecture of Mező which says that the hyperharmonic numbers – iterations of partial sums of harmonic numbers – are not integers. In this Note, using small intervals containing prime numbers, we prove that a great class of hyperharmonic numbers are not integers.

Dans un travail antérieur, les auteurs ont utilisé le postulat de Bertrand pour répondre, partiellement, à la conjecture de Mező selon laquelle les nombres hyperharmoniques – itérations de sommes partielles de nombres harmoniques – ne sont pas des entiers. Dans cette Note, nous montrons qu'une grande classe de nombres hyperharmoniques ne sont pas des entiers en utilisant les petits intervalles contenant des nombres premiers.

Received: 2010-10-26
Accepted: 2010-12-23
Published online: 2011-01-05

DOI: 10.1016/j.crma.2010.12.015

Author's affiliations:

Rachid Aït Amrane ¹ ; Hacène Belbachir ²

¹ ESI/École nationale supérieure d'informatique, BP 68M, Oued Smar, 16309, El Harrach, Alger, Algeria
² USTHB, faculté de mathématiques, BP 32, El Alia, 16111 Bab Ezzouar, Alger, Algeria

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Rachid Aït Amrane; Hacène Belbachir. Are the hyperharmonics integral? A partial answer via the small intervals containing primes. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 115-117. doi: 10.1016/j.crma.2010.12.015

References
Cited by

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