File Download
  Links for fulltext
     (May Require Subscription)
Supplementary

Article: The aliquot constant

TitleThe aliquot constant
Authors
Issue Date2012
Citation
Quarterly Journal of Mathematics, 2012, v. 63 n. 2, p. 309-323 How to Cite?
AbstractThe average value of log s(n)/n taken over the first N even integers is shown to converge to a constant λ when N tends to infinity; moreover, the value of this constant is approximated and proved to be less than 0. Here, s(n) sums the divisors of n less than n. Thus, the geometric mean of s(n)/n, the growth factor of the function s, in the long run tends to be less than 1. This could be interpreted as probabilistic evidence that aliquot sequences tend to remain bounded.
Persistent Identifierhttp://hdl.handle.net/10722/192200
ISSN
2015 Impact Factor: 0.853
2015 SCImago Journal Rankings: 1.289
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorBosma, Wen_US
dc.contributor.authorKane, Ben_US
dc.date.accessioned2013-10-23T09:27:19Z-
dc.date.available2013-10-23T09:27:19Z-
dc.date.issued2012en_US
dc.identifier.citationQuarterly Journal of Mathematics, 2012, v. 63 n. 2, p. 309-323en_US
dc.identifier.issn0033-5606en_US
dc.identifier.urihttp://hdl.handle.net/10722/192200-
dc.description.abstractThe average value of log s(n)/n taken over the first N even integers is shown to converge to a constant λ when N tends to infinity; moreover, the value of this constant is approximated and proved to be less than 0. Here, s(n) sums the divisors of n less than n. Thus, the geometric mean of s(n)/n, the growth factor of the function s, in the long run tends to be less than 1. This could be interpreted as probabilistic evidence that aliquot sequences tend to remain bounded.-
dc.languageengen_US
dc.relation.ispartofQuarterly Journal of Mathematicsen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleThe aliquot constanten_US
dc.typeArticleen_US
dc.description.naturepostprint-
dc.identifier.doi10.1093/qmath/haq050en_US
dc.identifier.scopuseid_2-s2.0-84861408925en_US
dc.identifier.volume63en_US
dc.identifier.issue2en_US
dc.identifier.spage309en_US
dc.identifier.epage323en_US
dc.identifier.isiWOS:000304197500003-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats