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

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

2005-03-13

arxiv.org/abs/math/0503246v1

Canad. J. Math. 59 (2007), 127-147

Mathematics

Number Theory

20 pages, see also http://www.dms.umontreal.ca/~lamzouri

Scientific paper

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.

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