login
A060606
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.
0
0, 1, 3, 5, 8, 10, 13, 16, 19, 22, 26, 29, 33, 36, 40, 44, 49, 52, 56, 60, 64, 68, 73, 77, 82, 86, 90, 94, 99, 103, 108, 113, 118, 123, 128, 132, 137, 141, 146, 151, 157, 161, 166, 171, 176, 181, 187, 192, 197, 202, 208, 213, 219, 223, 229, 234, 239, 244, 250, 255
OFFSET
0,3
LINKS
Hartosh Singh Bal, Gaurav Bhatnagar, Prime number conjectures from the Shapiro class structure, arXiv:1903.09619 [math.NT], 2019. See function S(n) p. 2.
Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.
Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]
H. Shapiro, An arithmetic function arising from Phi-function, American Math. Monthly 50:18-30.
FORMULA
a(n) = Sum_{j=1..n} A003434(j).
EXAMPLE
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.
CROSSREFS
Sequence in context: A245314 A186150 A377206 * A350234 A050504 A330038
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 13 2001
STATUS
approved