Hyperharmonic integers exist

Sertbas D. C.

COMPTES RENDUS MATHEMATIQUE, vol.358, no.11-12, pp.1179-1185, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 358 Issue: 11-12
  • Publication Date: 2020
  • Doi Number: 10.5802/crmath.137
  • Journal Name: COMPTES RENDUS MATHEMATIQUE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aquatic Science & Fisheries Abstracts (ASFA), MathSciNet, zbMATH
  • Page Numbers: pp.1179-1185
  • Çukurova University Affiliated: No

Abstract

We show that there exist infinitely many hyperharmonic integers, and this refutes a conjecture of Mezo. In particular, for r = 64.(2(alpha)-1)+32, the hyperharmonic number h(33)((r)) is integer for 153 different values of alpha (mod 748440), where the smallest r is equal to 64.(2(2659)-1)+32.