no. 11-12
Théorie des nombres
Hyperharmonic integers exist
[Des entiers hyperharmoniques existent]
Sertbaş, Doğa Can1
1 Department of Mathematics, Faculty of Sciences, Sivas Cumhuriyet University, 58140, Sivas, TURKEY.
Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1179-1185.

We show that there exist infinitely many hyperharmonic integers, and this refutes a conjecture of Mező. In particular, for r=64·(2 α -1)+32, the hyperharmonic number h 33 (r) is integer for 153 different values of α(mod748440), where the smallest r is equal to 64·(2 2659 -1)+32.

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DOI : 10.5802/crmath.137
Classification : 11B83, 05A10, 11B75
Sertbaş, Doğa Can 1

1 Department of Mathematics, Faculty of Sciences, Sivas Cumhuriyet University, 58140, Sivas, TURKEY. 
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Sertbaş, Doğa Can. Hyperharmonic integers exist. Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1179-1185. doi : 10.5802/crmath.137. http://www.numdam.org/articles/10.5802/crmath.137/

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