Density results on hyperharmonic integers

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dc.authorscopusidDoğa Can Sertbaş / 57191499222
dc.authorwosidDoğa Can Sertbaş / JSK-6611-2023
dc.contributor.authorSertbaş, Doğa Can
dc.date.accessioned2025-04-18T08:49:11Z
dc.date.available2025-04-18T08:49:11Z
dc.date.issued2025
dc.departmentİstinye Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümü
dc.description.abstractIt was conjectured that there are no hyperharmonic integers h(nr) except 1. In 2020, a disproof of this conjecture was given by showing the existence of infinitely many hyperharmonic integers. However, the corresponding proof does not give any general density results related to hyperharmonic integers. In this paper, we first get better error estimates for the counting function of the pairs (n, r) that correspond to non-integer hyperharmonic numbers using sums on gaps between consecutive prime numbers. Then, based on a plausible assumption on prime powers with restricted digits, we show that there exist positive integers n such that the set of positive integers r where h(nr) ∈ Z has positive density. Apart from that, we also obtain exact densities of sets {r ∈ Z>0: h(33r) ∈ Z} and {r ∈ Z>0: h(39r) ∈ Z}. Finally, we give the smallest hyperharmonic integer h(nr) greater than 1, which is obtained when n = 33 and r = 10 667 968. ©2025 The Mathematical Society of Japan.
dc.identifier.citationSertbaş, D. C. (2025). Density results on hyperharmonic integers. Journal of the Mathematical Society of Japan, 77(1), 189-219.
dc.identifier.doi10.2969/jmsj/91179117
dc.identifier.endpage219
dc.identifier.issn00255645
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85216888226
dc.identifier.scopusqualityQ2
dc.identifier.startpage189
dc.identifier.urihttp://dx.doi.org/10.2969/jmsj/91179117
dc.identifier.urihttps://hdl.handle.net/20.500.12713/6619
dc.identifier.volume77
dc.indekslendigikaynakScopus
dc.institutionauthorSertbaş, Doğa Can
dc.institutionauthoridDoğa Can Sertbaş / 0000-0002-5884-6856
dc.language.isoen
dc.publisherMathematical Society of Japan
dc.relation.ispartofJournal of the Mathematical Society of Japan
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectHyperharmonic Numbers
dc.subjectİntegerness Property
dc.subjectPrime Numbers
dc.titleDensity results on hyperharmonic integers
dc.typeArticle

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