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#### Article: The aliquot constant

Title The aliquot constant Bosma, WKane, B 2012 Quarterly Journal of Mathematics, 2012, v. 63 n. 2, p. 309-323 How to Cite? The 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. http://hdl.handle.net/10722/192200 0033-56062015 Impact Factor: 0.8532015 SCImago Journal Rankings: 1.289 WOS:000304197500003

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.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-