The Index of Composition of the Iterates of the Euler Function
نویسنده
چکیده
The index of composition of an integer n ≥ 2 is defined as λ(n) = (log n)/(log γ(n)), where γ(n) stands for the largest square-free divisor of n. Let φ stand for the Euler totient function. We show that the index of composition of the k-fold iterate of φ(n) is 1 on a set of density 1 and that an analogous result holds if n runs over the set of shifted primes.
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