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dc.contributor.authorBagdasar, Ovidiu
dc.contributor.authorTatt, Ralph-Joseph
dc.date.accessioned2018-12-17T14:23:26Z
dc.date.available2018-12-17T14:23:26Z
dc.date.issued2018-12-06
dc.identifier.citationBagdasar, O., and Tatt, R. (2018) ‘On some new arithmetic functions involving prime divisors and perfect powers’, Electronic Notes in Discrete Mathematics, 70, pp.9-15. doi: 10.1016/j.endm.2018.11.002en
dc.identifier.issn1571-0653
dc.identifier.doi10.1016/j.endm.2018.11.002
dc.identifier.urihttp://hdl.handle.net/10545/623232
dc.description.abstractInteger division and perfect powers play a central role in numerous mathematical results, especially in number theory. Classical examples involve perfect squares like in Pythagora’s theorem, or higher perfect powers as the conjectures of Fermat (solved in 1994 by A. Wiles [8]) or Catalan (solved in 2002 by P. Mih˘ailescu [4]). The purpose of this paper is two-fold. First, we present some new integer sequences a(n), counting the positive integers smaller than n, having a maximal prime factor. We introduce an arithmetic function counting the number of perfect powers i j obtained for 1 ≤ i, j ≤ n. Along with some properties of this function, we present the sequence A303748, which was recently added to the Online Encyclopedia of Integer Sequences (OEIS) [5]. Finally, we discuss some other novel integer sequences.
dc.description.sponsorshipO. Bagdasar’s research was supported by a grant of the Roma- nian National Authority for Research and Innovation, CNCS/CCCDI UEFISCDI, project number PN-III-P2-2.1-PED-2016-1835, within PNCDI III.en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.ispartofseriesProceedings of TCDM'18en
dc.relation.urlhttps://www.sciencedirect.com/science/article/pii/S1571065318301975en
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectArithmetic functionsen
dc.subjectPerfect powersen
dc.subjectInteger sequencesen
dc.titleOn some new arithmetic functions involving prime divisors and perfect powers.en
dc.typeArticleen
dc.contributor.departmentUniversity of Derbyen
dc.identifier.journalElectronic Notes in Discrete Mathematicsen
html.description.abstractInteger division and perfect powers play a central role in numerous mathematical results, especially in number theory. Classical examples involve perfect squares like in Pythagora’s theorem, or higher perfect powers as the conjectures of Fermat (solved in 1994 by A. Wiles [8]) or Catalan (solved in 2002 by P. Mih˘ailescu [4]). The purpose of this paper is two-fold. First, we present some new integer sequences a(n), counting the positive integers smaller than n, having a maximal prime factor. We introduce an arithmetic function counting the number of perfect powers i j obtained for 1 ≤ i, j ≤ n. Along with some properties of this function, we present the sequence A303748, which was recently added to the Online Encyclopedia of Integer Sequences (OEIS) [5]. Finally, we discuss some other novel integer sequences.


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