Generating functions for divisor sums and totative sums arising from combinatorial Simsek numbers

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dc.contributor.authorKucukoglu, Irem
dc.date.accessioned2026-01-24T12:29:21Z
dc.date.available2026-01-24T12:29:21Z
dc.date.issued2024
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractThe main objective of this paper is to introduce and investigate new number families derived from finite sums running over divisors and totatives and containing higher powers of binomial coefficients. Especially, by making decomposition on the generating functions for a kind of combinatorial number families recently introduced by Simsek [29], we also construct generating functions for the newly introduced number families. For symbolic computation of the newly introduced number families and their generating functions, we also give computational implementations in the Wolfram language. By these implementations, some tables of both these number families and their generating functions have been presented for some arbitrarily chosen special cases. Additionally, we provide some applications regarding the Thacker's (totient) function. In particular, by making summation on all totatives of a positive integer, we investigate some special finite sums containing both the Thacker's (totient) function and higher powers of binomial coefficients. By this investigation, some of the problems regarding these finite sums have been partially answered accompanied by some remarks. Furthermore, we propose an open problem regarding a potential relation between one of these number families and a formula involving the Mo center dot bius function. Finally, the paper have been concluded by providing an overview on the results of this paper and their potential usage areas, and by making suggestions regarding future studies able to be made.
dc.identifier.doi10.2298/FIL2405513K
dc.identifier.endpage1529
dc.identifier.issn0354-5180
dc.identifier.issue5
dc.identifier.scopus2-s2.0-85187911672
dc.identifier.scopusqualityQ2
dc.identifier.startpage1513
dc.identifier.urihttps://doi.org/10.2298/FIL2405513K
dc.identifier.urihttps://hdl.handle.net/20.500.12868/5304
dc.identifier.volume38
dc.identifier.wosWOS:001127083100001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherUniv Nis, Fac Sci Math
dc.relation.ispartofFilomat
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260121
dc.subject. Binomial coefficients
dc.subjectComputational implementations
dc.subjectDivisor sums
dc.subjectGeneralized Franel numbers
dc.subjectGenerating func-tion
dc.subjectSpecial numbers
dc.subjectCombinatorial Simsek numbers
dc.subjectNumber-theoretic (arithmetical) functions
dc.subjectMo center dot bius function
dc.subjectEuler's totient function
dc.subjectThacker's (totient) function
dc.subjectTotatives
dc.titleGenerating functions for divisor sums and totative sums arising from combinatorial Simsek numbers
dc.typeArticle

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