Mathematical Journal of Okayama University 59巻 1号
2017-01 発行

An arithmetic function arising from the Dedekind ψ function

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 S1, S2, S3 and determine some properties of these sets.
Keywords
Iterated function
Dedekind function
additive function