publication . Preprint . 2005

Smooth values of the iterates of the Euler's Phi function

Lamzouri, Youness;
Open Access English
  • Published: 13 Mar 2005
Let $\phi(n)$ be the Euler-phi function, define $\phi_0(n) = n$ and $\phi_{k+1}(n)=\phi(\phi_{k}(n))$ for all $k\geq 0$. We will determine an asymptotic formula for the set of integers $n$ less than $x$ for which $\phi_k(n)$ is $y$-smooth, conditionally on a weak form of the Elliott-Halberstam conjecture.
free text keywords: Mathematics - Number Theory, 11N37, 11B37, 34K05, 45J05
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