Superharmonic numbers

Cohen, GL

Superharmonic numbers

Cohen, GL

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Publication Type:: Journal Article
Citation:: Mathematics of Computation, 2009, 78 (265), pp. 421 - 429
Issue Date:: 2009-01-12

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Field	Value	Language
dc.contributor.author	Cohen, GL	en_US
dc.date.issued	2009-01-12	en_US
dc.identifier.citation	Mathematics of Computation, 2009, 78 (265), pp. 421 - 429	en_US
dc.identifier.issn	0025-5718	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8271
dc.description.abstract	Let τ(n) denote the number of positive divisors of a natural number n > 1 and let σ(n) denote their sum. Then n is superharmonic if σ(n) \| nκτ(n) for some positive integer κ. We deduce numerous properties of superharmonic numbers and show in particular that the set of all superharmonic numbers is the first nontrivial example that has been given of an infinite set that contains all perfect numbers but for which it is difficult to determine whether there is an odd member. © 2008 American Mathematical Society.	en_US
dc.relation.ispartof	Mathematics of Computation	en_US
dc.relation.isbasedon	10.1090/S0025-5718-08-02147-9	en_US
dc.subject.classification	Numerical & Computational Mathematics	en_US
dc.title	Superharmonic numbers	en_US
dc.type	Journal Article
utslib.citation.volume	265	en_US
utslib.citation.volume	78	en_US
utslib.for	0103 Numerical and Computational Mathematics	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
dc.location.activity	ISI:000260130200021	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical Sciences
utslib.copyright.status	open_access
pubs.issue	265	en_US
pubs.publication-status	Published	en_US
pubs.volume	78	en_US

Abstract:

Let τ(n) denote the number of positive divisors of a natural number n > 1 and let σ(n) denote their sum. Then n is superharmonic if σ(n) | nκτ(n) for some positive integer κ. We deduce numerous properties of superharmonic numbers and show in particular that the set of all superharmonic numbers is the first nontrivial example that has been given of an infinite set that contains all perfect numbers but for which it is difficult to determine whether there is an odd member. © 2008 American Mathematical Society.

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http://hdl.handle.net/10453/8271