Mathematical Journal of Okayama University 59巻 1号

2017-01 発行

Defant, Colin
Department of Mathematics, University of Florida

Publication Date

2017-01

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 *S*_{1}, S_{2}, S_{3} and determine some properties of these sets.

for all primes

Keywords

Iterated function

Dedekind function

additive function