cp's OEIS Frontend

A060605 a(n) = sum of lengths of the iteration sequences of Euler totient function from 1 to n.

%I A060605 #22 Mar 23 2024 12:56:48
%S A060605 1,3,6,9,13,16,20,24,28,32,37,41,46,50,55,60,66,70,75,80,85,90,96,101,
%T A060605 107,112,117,122,128,133,139,145,151,157,163,168,174,179,185,191,198,
%U A060605 203,209,215,221,227,234,240,246,252,259,265,272,277,284,290,296,302
%N A060605 a(n) = sum of lengths of the iteration sequences of Euler totient function from 1 to n.
%C A060605 Partial sums of A049108. - _Joerg Arndt_, Jan 06 2015
%H A060605 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 A060605 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]
%H A060605 Harold Shapiro, <a href="http://www.jstor.org/stable/2303988">An arithmetic function arising from the phi function</a>, Amer. Math. Monthly, Vol. 50, No. 1 (1943), 18-30.
%F A060605 a(n) = sum( j=1..n, A049108(j) ).
%e A060605 Iteration sequences of Phi applied to 1, 2, 3, 4, 5, 6 give lengths 1, 2, 3, 3, 4, 3 with partial sums as follows:1, 3, 5, 9, 13, 16 resulting in first...6th terms here.
%t A060605 Accumulate[Table[Length[NestWhileList[EulerPhi,n,#!=1&]],{n,60}]] (* _Harvey P. Dale_, Mar 23 2024 *)
%o A060605 (PARI) a049108(n)=my(t=1); while(n>1, t++; n=eulerphi(n)); t;
%o A060605 vector(80, n, sum(j=1, n, a049108(j))) \\ _Michel Marcus_, Jan 06 2015
%Y A060605 Cf. A049108, A003434.
%K A060605 nonn
%O A060605 1,2
%A A060605 _Labos Elemer_, Apr 13 2001