Compositions with the Euler and Carmichael Functions

Compositions with the Euler and Carmichael Functions

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by W. D. Banks , F. Luca , F. Saidak , P. Stănică

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@MISC{Banks_compositionswith,
    author = {W. D. Banks and F. Luca and F. Saidak and P. Stănică},
    title = {Compositions with the Euler and Carmichael Functions},
    year = {}
}

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Abstract

Abstract. Let ϕ and λ be the Euler and Carmichael functions, respectively. In this paper, we establish lower and upper bounds for the number of positive integers n ≤ x such that ϕ(λ(n)) = λ(ϕ(n)). We also study the normal order of the function ϕ(λ(n))/λ(ϕ(n)). 1

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