On the ratio of the sum of divisors and Euler’s Totient Function I

Simple item page
dc.contributor.authorBroughan, Kevin A.
dc.contributor.authorDelbourgo, Daniel
dc.date.accessioned2014-01-28T02:07:48Z
dc.date.available2014-01-28T02:07:48Z
dc.date.issued2013
dc.description.abstractWe prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factors are 3, 35 and 1045. Moreover, there exist at most a finite number of solutions to σ(n)=2φ(n) with Ω(n)≤ k, and there are at most 22k+k-k squarefree solutions to φ (n)|σ(n) if ω(n)=k. Lastly the number of solutions to φ(n)|φ(n) as x→∞ is O(x exp(-½√log x)).en_NZ
dc.format.mimetypeapplication/pdf
dc.identifier.citationBroughtan, K. A. & Delbourgo, D. (2013). On the ratio of the sum of divisors and Euler’s Totient Function I. Journal of Integer Sequences, 16, article 13.8.8.en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/8429
dc.language.isoenen_NZ
dc.relation.isPartOfJournal of Integer Sequencesen_NZ
dc.relation.urihttps://cs.uwaterloo.ca/journals/JIS/VOL16/Broughan/broughan26.htmlen_NZ
dc.rightsThis article has been published in the Journal of Integer Sequences. © 2013 the authors.en_NZ
dc.subjectmathematicsen_NZ
dc.titleOn the ratio of the sum of divisors and Euler’s Totient Function Ien_NZ
dc.typeJournal Articleen_NZ
pubs.begin-page1en_NZ
pubs.editionArticle 13.8.8en_NZ
pubs.elements-id38913
pubs.end-page16en_NZ
pubs.issue8en_NZ
pubs.volume16en_NZ
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
on the Ratio.pdf
Size:
189.71 KB
Format:
Adobe Portable Document Format
Description:
Thumbnail Image
Name: on the Ratio.pdf
Size: 189.71 KB
Kind: Adobe PDF
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.71 KB
Format:
Item-specific license agreed upon to submission
Description:
Name: license.txt
Size: 1.71 KB
Kind: License
Collections
Computing and Mathematical Sciences Papers