Hyperharmonic integers exist

Doğa Can Sertbaş

doi:10.5802/crmath.137

Théorie des nombres

Hyperharmonic integers exist
[Des entiers hyperharmoniques existent]

Doğa Can Sertbaş ¹

¹ Department of Mathematics, Faculty of Sciences, Sivas Cumhuriyet University, 58140, Sivas, TURKEY.

Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1179-1185.

Résumé

We show that there exist infinitely many hyperharmonic integers, and this refutes a conjecture of Mező. In particular, for $r = 64 \cdot (2^{α} - 1) + 32$ , the hyperharmonic number $h_{33}^{(r)}$ is integer for 153 different values of $α (mod 748 440)$ , where the smallest $r$ is equal to $64 \cdot (2^{2659} - 1) + 32$ .

Reçu le : 2020-02-12
Révisé le : 2020-07-20
Accepté le : 2020-10-23
Publié le : 2021-01-25

DOI : 10.5802/crmath.137

Classification : 11B83, 05A10, 11B75

Affiliations des auteurs :

Doğa Can Sertbaş ¹

¹ Department of Mathematics, Faculty of Sciences, Sivas Cumhuriyet University, 58140, Sivas, TURKEY.

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Hyperharmonic integers exist},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1179--1185},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {11-12},
     year = {2020},
     doi = {10.5802/crmath.137},
     language = {en},
}

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Doğa Can Sertbaş. Hyperharmonic integers exist. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1179-1185. doi : 10.5802/crmath.137. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.137/

Bibliographie
Cité par

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Doğa Can Sertbaş Density results on hyperharmonic integers, Journal of the Mathematical Society of Japan, Volume 77 (2025) no. 1, pp. 189-219 | DOI:10.2969/jmsj/91179117 | Zbl:8012149
Çağatay Altuntaş On the finiteness of some p-divisible sets, Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, Volume 73 (2024) no. 4, p. 1011 | DOI:10.31801/cfsuasmas.1441894
Çağatay Altuntaş On the $p$ -adic valuation of generalized harmonic numbers, Bulletin of the Korean Mathematical Society, Volume 60 (2023) no. 4, pp. 933-955 | DOI:10.4134/bkms.b220399 | Zbl:1539.11045
Çağatay Altuntaş; Haydar Göral; Doğa Can Sertbaş The difference of hyperharmonic numbers via geometric and analytic methods, Journal of the Korean Mathematical Society, Volume 59 (2022) no. 6, pp. 1103-1137 | DOI:10.4134/jkms.j210630 | Zbl:1522.11014
Haydar Göral; Doğa Can Sertbaş Applications of class numbers and Bernoulli numbers to harmonic type sums, Bulletin of the Korean Mathematical Society, Volume 58 (2021) no. 6, pp. 1463-1481 | DOI:10.4134/bkms.b201045 | Zbl:1496.11034

Cité par 5 documents. Sources : Crossref, zbMATH

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