Compositions with the euler and carmichael functions |
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| Authors: | W D Banks F Luca F Saidak P StĂ;nicĂ |
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| Institution: | (1) Department of Mathematics, University of Missouri, 65211 Columbia, MO, USA;(2) Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México;(3) Department of Mathematics, Wake Forest University, 27109 Winston-Salem, NC, USA;(4) Mathematics Department, Auburn University Montgomery, 36124 Montgomery, AL, USA |
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| 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)). |
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