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%I #16 Sep 08 2021 07:13:45
%S 1,2,2,3,3,2,2,4,2,3,3,3,3,2,4,5,5,2,2,4,3,3,3,4,4,3,2,3,3,4,4,6,4,5,
%T 4,3,3,2,4,5,5,3,3,4,4,3,3,5,3,4,6,4,4,2,5,4,3,3,3,5,5,4,3,7,5,4,4,6,
%U 4,4,4,4,4,3,5,3,5,4,4,6,2,5,5,4,7,3,4,5,5,4,4,4,5,3,4,6,6,3,5,5,5,6,6,5,5
%N Number of powers of 2 in sequence obtained when phi (A000010) is repeatedly applied to n.
%F a(n) = A049108(n)-A049115(n). - _R. J. Mathar_, Sep 08 2021
%e If n=164, the "iterated phi-sequence" for n is {164,80,32,16,8,4,2,1}. It includes 6 powers of 2 at the end, so a(164)=6.
%p A049113 := proc(n)
%p local a, e;
%p e := n ;
%p a :=0 ;
%p while e > 1 do
%p if isA000079(e) then
%p a := a+1 ;
%p end if;
%p e := numtheory[phi](e) ;
%p end do:
%p 1+a;
%p end proc:
%p seq(A049113(n),n=1..40) ; # _R. J. Mathar_, Jan 09 2017
%t pwrs2 = NestList[2#&, 1, 15];
%t Table[Length[Intersection[NestWhileList[EulerPhi[#]&, i, # > 1 &], pwrs2]], {i, 100}] (* _Harvey P. Dale_, Dec 12 2010 *)
%o (PARI) a(n)=while(n!=1<<valuation(n,2),n=eulerphi(n)); valuation(n,2)+1 \\ _Charles R Greathouse IV_, Feb 21 2013
%Y Cf. A000010, A049115, A049108.
%K nonn
%O 1,2
%A _Labos Elemer_
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