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A184968 Smallest k such that phi(phi(k)) = 2^n, where phi is the Euler totient function.

%I A184968 #20 Nov 15 2024 07:00:05
%S A184968 5,11,17,41,85,137,257,641,1285,2329,4369,10537,17477,35209,65537,
%T A184968 163841,297109,557057,1114129,2687017,4491589,8978569,16843009,
%U A184968 42009217,71304257,143163649,286331153,690563369,1145390149,2281701377,4295098369,10737647617
%N A184968 Smallest k such that phi(phi(k)) = 2^n, where phi is the Euler totient function.
%H A184968 Robert Israel, <a href="/A184968/b184968.txt">Table of n, a(n) for n = 1..1000</a>
%H A184968 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%e A184968 a(5) = 85 because phi(85) = 64, phi(64) = 2^5.
%p A184968 with(numtheory):for n from 1 to 22 do: id:=0:for k from 1 to 10000000 while(id=0)
%p A184968   do: if phi(phi(k)) =2^n then id:=1:print(k):else fi:od:od:
%p A184968 # Alternative:
%p A184968 f:= proc(n) local S,s,r;
%p A184968   uses numtheory;
%p A184968   S:= sort(convert(invphi(2^n),list));
%p A184968   r:= infinity;
%p A184968   for s in S while s < r do
%p A184968     r:= min(r, min(invphi(s)))
%p A184968   od;
%p A184968   r
%p A184968 end proc:
%p A184968 map(f, [$1..50]); # _Robert Israel_, Mar 22 2017
%o A184968 (PARI) a(n) = {my(v = invphi(2^n), m); for(i = 1, #v, m = invphiMin(v[i]); v[i] = max(m, 0)); vecmin(select(x -> x > 0, v)); } \\ _Amiram Eldar_, Nov 15 2024, using _Max Alekseyev_'s invphi.gp
%Y A184968 Cf. A000010, A010554.
%K A184968 nonn
%O A184968 1,1
%A A184968 _Michel Lagneau_, Mar 27 2011
%E A184968 a(23)-a(32) from _Donovan Johnson_, Jul 28 2011