Abstract
Let \(\varphi _j (n)\) be the j-fold iterated function of \(\varphi (n)\). Let \(k \in \mathbb{N}\) and ε > 0 be fixed, Q be a prime, and let N k(Q|x) denote the number of those n≤x for which Q ∤ \(\varphi _{k + 1} (n)\). We give the asymptotics of N k(Q|x) in the range \(Q \in \left( {\left( {log log x} \right)^{k + \varepsilon } ,\left( {log log x} \right)^{k + 1 - \varepsilon } } \right)\).
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Indlekofer, KH., Kátai, I. On the Normal Order of ϕk+1(n)/ϕk(n), where ϕk is the k-Fold Iterate of Euler's Function. Lithuanian Mathematical Journal 44, 47–61 (2004). https://doi.org/10.1023/B:LIMA.0000019856.89380.72
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DOI: https://doi.org/10.1023/B:LIMA.0000019856.89380.72