このエントリーをはてなブックマークに追加
ID 54715
FullText URL
Author
Defant, Colin Department of Mathematics, University of Florida
Abstract
We define ψ‾ to be the multiplicative arithmetic function that satisfies

for all primes p and positive integers α. Let λ(n) be the number of iterations of the function ψ‾ needed for n to reach 2. It follows from a theorem due to White that λ is additive. Following Shapiro's work on the iterated φ function, we determine bounds for λ. We also use the function λ to partition the set of positive integers into three sets S1, S2, S3 and determine some properties of these sets.
Keywords
Iterated function
Dedekind function
additive function
Published Date
2017-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume59
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
81
End Page
92
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
Official Url
http://www.math.okayama-u.ac.jp/mjou/
language
英語
Copyright Holders
Copyright©2017 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol59/iss1/6