Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1093/qmath/haq050
- Scopus: eid_2-s2.0-84861408925
- WOS: WOS:000304197500003
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: The aliquot constant
Title | The aliquot constant |
---|---|
Authors | |
Issue Date | 2012 |
Citation | Quarterly Journal of Mathematics, 2012, v. 63 n. 2, p. 309-323 How to Cite? |
Abstract | 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. |
Persistent Identifier | http://hdl.handle.net/10722/192200 |
ISSN | 2023 Impact Factor: 0.6 2023 SCImago Journal Rankings: 0.378 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Bosma, W | en_US |
dc.contributor.author | Kane, B | en_US |
dc.date.accessioned | 2013-10-23T09:27:19Z | - |
dc.date.available | 2013-10-23T09:27:19Z | - |
dc.date.issued | 2012 | en_US |
dc.identifier.citation | Quarterly Journal of Mathematics, 2012, v. 63 n. 2, p. 309-323 | en_US |
dc.identifier.issn | 0033-5606 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/192200 | - |
dc.description.abstract | 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. | - |
dc.language | eng | en_US |
dc.relation.ispartof | Quarterly Journal of Mathematics | en_US |
dc.title | The aliquot constant | en_US |
dc.type | Article | en_US |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1093/qmath/haq050 | en_US |
dc.identifier.scopus | eid_2-s2.0-84861408925 | en_US |
dc.identifier.volume | 63 | en_US |
dc.identifier.issue | 2 | en_US |
dc.identifier.spage | 309 | en_US |
dc.identifier.epage | 323 | en_US |
dc.identifier.isi | WOS:000304197500003 | - |
dc.identifier.issnl | 0033-5606 | - |