On perfect totient numbers

Iannucci, DE; Moujie, D; Cohen, GL

On perfect totient numbers

Iannucci, DE Moujie, D Cohen, GL

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Publication Type:: Journal Article
Citation:: Journal of Integer Sequences, 2003, 6 (4)
Issue Date:: 2003-12-01

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Field	Value	Language
dc.contributor.author	Iannucci, DE	en_US
dc.contributor.author	Moujie, D	en_US
dc.contributor.author	Cohen, GL	en_US
dc.date.issued	2003-12-01	en_US
dc.identifier.citation	Journal of Integer Sequences, 2003, 6 (4)	en_US
dc.identifier.issn	1530-7638	en_US
dc.identifier.uri	http://hdl.handle.net/10453/5644
dc.description.abstract	Let n > 2 be a positive integer and let φ denote Euler's totient function. Define φ1(n) = φ(n) and φk(n) = φ(φk-1(n)) for all integers k ≥ 2. Define the arithmetic function S by S(n) = φ(n) + φ2(n) +...+ φc(n) + 1, where φc(n) = 2. We say n is a perfect totient number if S(n) = n. We give a list of known perfect totient numbers, and we give sufficient conditions for the existence of further perfect totient numbers.	en_US
dc.relation.ispartof	Journal of Integer Sequences	en_US
dc.subject.classification	Computation Theory & Mathematics	en_US
dc.title	On perfect totient numbers	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	6	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0103 Numerical and Computational Mathematics	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	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	6	en_US

Abstract:

Let n > 2 be a positive integer and let φ denote Euler's totient function. Define φ1(n) = φ(n) and φk(n) = φ(φk-1(n)) for all integers k ≥ 2. Define the arithmetic function S by S(n) = φ(n) + φ2(n) +...+ φc(n) + 1, where φc(n) = 2. We say n is a perfect totient number if S(n) = n. We give a list of known perfect totient numbers, and we give sufficient conditions for the existence of further perfect totient numbers.

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http://hdl.handle.net/10453/5644