Hyperharmonic integers exist

Sertbas D. C.

COMPTES RENDUS MATHEMATIQUE, cilt.358, sa.11-12, ss.1179-1185, 2020 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 358 Sayı: 11-12
  • Basım Tarihi: 2020
  • Doi Numarası: 10.5802/crmath.137
  • Dergi Adı: COMPTES RENDUS MATHEMATIQUE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aquatic Science & Fisheries Abstracts (ASFA), MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1179-1185
  • Çukurova Üniversitesi Adresli: Hayır

Özet

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.