cp's OEIS Frontend

A289125 Numbers n such that phi(n)/phi(phi(n)) > phi(m)/phi(phi(m)) for all m < n.

%I A289125 #18 Aug 17 2024 19:02:28
%S A289125 1,3,7,31,211,2311,43891,60653,870871,1023053,13123111,19417793,
%T A289125 300690391,446235509,6915878971,12939711677,200560490131
%N A289125 Numbers n such that phi(n)/phi(phi(n)) > phi(m)/phi(phi(m)) for all m < n.
%C A289125 Erdős et al. proved that phi(n)/phi(phi(n)) is unbounded, thus this sequence is infinite.
%C A289125 A018239(k) = A002110(A014545(k)) + 1 is a term for k > 1. Are there terms m with omega(m) > 2? Is omega(phi(a(n + 1))) >= omega(phi(a(n)))? - _David A. Corneth_, Jun 28 2017
%H A289125 Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, <a href="http://math.dartmouth.edu/~carlp/iterate.pdf">On the normal behavior of the iterates of some arithmetic functions</a>, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.
%H A289125 Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, <a href="/A000010/a000010_1.pdf">On the normal behavior of the iterates of some arithmetic functions</a>, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]
%t A289125 a = {}; k=1; rmax = 0; While[Length[a]<10,s = EulerPhi[ k]; s2 = EulerPhi[ s]; r = s/s2;  If[r > rmax, AppendTo[a, k]; rmax = r]; k++]; a
%t A289125 DeleteDuplicates[Table[{n,EulerPhi[n]/EulerPhi[EulerPhi[n]]},{n,11*10^5}],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* The program generates the first ten terms of the sequence. *) (* _Harvey P. Dale_, Aug 17 2024 *)
%o A289125 (PARI) r=0; forfactored(n=1,10^10, t=eulerphi(n); t/=eulerphi(t); if(t>r, r=t; print1(n[1]", "))) \\ _Charles R Greathouse IV_, Jun 25 2017
%Y A289125 Cf. A000010, A001221, A002110, A010554, A014545, A018239.
%K A289125 nonn,more
%O A289125 1,2
%A A289125 _Amiram Eldar_, Jun 25 2017
%E A289125 a(15)-a(17) from _Giovanni Resta_, Jul 01 2017