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dc.contributor.authorBroughan, Kevin A.en_NZ
dc.contributor.authorDelbourgo, Danielen_NZ
dc.contributor.authorZhou, Qizhien_NZ
dc.date.accessioned2017-09-12T23:17:49Z
dc.date.available2014-04-01en_NZ
dc.date.available2017-09-12T23:17:49Z
dc.date.issued2014en_NZ
dc.identifier.citationBroughan, K. A., Delbourgo, D., & Zhou, Q. (2014). A conjecture of De Koninck regarding particular square values of the sum of divisors function. Journal of Number Theory, 137, 50–66. https://doi.org/10.1016/j.jnt.2013.10.011en
dc.identifier.issn0022-314Xen_NZ
dc.identifier.urihttp://hdl.handle.net/10289/11326
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. If the prime dividing a solution n is congruent to 3 modulo 8 then it must be greater than 41, and every solution is divisible by at least the fourth power of an odd prime. Moreover at least 2/5 of the exponents a of the primes dividing any solution have the property that a + 1 is a prime power. Lastly we prove that the number of solutions up to x > 1 is at most x¹/⁶⁺є, for any є > 0 and all x > xє.
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.publisherElsevier Incen_NZ
dc.rightsThis is an author’s accepted version of an article published in the journal: Journal of Number Theory. © 2013 Elsevier Inc.
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectMathematicsen_NZ
dc.subjectSum of divisorsen_NZ
dc.subjectSquarefrce coreen_NZ
dc.subjectDe Koninck's conjectureen_NZ
dc.subjectCompactificationen_NZ
dc.subjectPerfect numbersen_NZ
dc.titleA conjecture of De Koninck regarding particular square values of the sum of divisors functionen_NZ
dc.typeJournal Article
dc.identifier.doi10.1016/j.jnt.2013.10.011en_NZ
dc.relation.isPartOfJournal of Number Theoryen_NZ
pubs.begin-page50
pubs.elements-id39151
pubs.end-page66
pubs.organisational-group/Waikato
pubs.organisational-group/Waikato/2018 PBRF
pubs.organisational-group/Waikato/FCMS
pubs.organisational-group/Waikato/FCMS/2018 PBRF - FCMS
pubs.publication-statusPublisheden_NZ
pubs.volume137en_NZ
dc.identifier.eissn1096-1658en_NZ


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