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%I #18 Mar 26 2019 15:55:05
%S 0,1,3,5,8,10,13,16,19,22,26,29,33,36,40,44,49,52,56,60,64,68,73,77,
%T 82,86,90,94,99,103,108,113,118,123,128,132,137,141,146,151,157,161,
%U 166,171,176,181,187,192,197,202,208,213,219,223,229,234,239,244,250,255
%N The n-th term is the sum of lengths of iteration chains to get fixed points(=1) for the Euler totient function from 1 to n.
%H Hartosh Singh Bal, Gaurav Bhatnagar, <a href="https://arxiv.org/abs/1903.09619">Prime number conjectures from the Shapiro class structure</a>, arXiv:1903.09619 [math.NT], 2019. See function S(n) p. 2.
%H 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 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 H. Shapiro, <a href="https://www.jstor.org/stable/2303988">An arithmetic function arising from Phi-function</a>, American Math. Monthly 50:18-30.
%F a(n) = Sum_{j=1..n} A003434(j).
%e Iteration sequences of Phi applied to 1,2,3,4,5,6 give lengths 0,1,2,2,3,2 with partial sums as follows:0,1,3,5,8,10 resulting in the first six terms of this sequence. It differs by n from the analogous sums applied to A049108 sequence.
%Y Cf. A003434, A049108.
%K nonn
%O 0,3
%A _Labos Elemer_, Apr 13 2001
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