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dc.contributor.authorBroughan, Kevin A.
dc.contributor.authorDe Koninck, Jean-Marie
dc.contributor.authorK´atai, Imre
dc.contributor.authorLuca, Florian
dc.date.accessioned2013-02-25T02:18:02Z
dc.date.available2013-02-25T02:18:02Z
dc.date.issued2012
dc.identifier.citationBroughan, K.A., De Koninck. J-M., K´atai, I. & Luca, F. (2012). On integers for which the sum of divisors is the square of the squarefree core. Journal of Integer Sequences, 15(7), 1-12.en_NZ
dc.identifier.issn1530-7638
dc.identifier.urihttps://hdl.handle.net/10289/7248
dc.description.abstractWe study integers n > 1 satisfying the relation σ(n) = γ(n) ² , where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. We show that the only solution n with at most four distinct prime factors is n = 1782. We show that there is no solution which is fourth power free. We also show that the number of solutions up to x > 1 is at most x ⅟⁴⁺ᵉ for any ε > 0 and all x > xε. Further, call n primitive if no proper unitary divisor d of n satisfies σ(d) | γ(d) ² . We show that the number of primitive solutions to the equation up to x is less than xᵉ for x > xₑ.en_NZ
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherUniversity of Waterlooen_NZ
dc.relation.urihttps://cs.uwaterloo.ca/journals/JIS/vol15.htmlen_NZ
dc.rights© 2012, The Authors.en_NZ
dc.subjectmathematicsen_NZ
dc.subjectintegersen_NZ
dc.subjectnumber theoryen_NZ
dc.titleOn integers for which the sum of divisors is the square of the squarefree coreen_NZ
dc.typeJournal Articleen_NZ
dc.relation.isPartOfJournal of Integer Sequenceen_NZ
pubs.begin-page1en_NZ
pubs.editionSeptemberen_NZ
pubs.elements-id37967
pubs.end-page12en_NZ
pubs.issue7en_NZ
pubs.volume15en_NZ


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