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A185816 Number of iterations of lambda(n) needed to reach 1. 6
0, 1, 2, 2, 3, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 3, 4, 3, 4, 3, 3, 4, 5, 2, 4, 3, 4, 3, 4, 3, 4, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 3, 4, 4, 3, 5, 6, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 5, 3, 4, 4, 3, 4, 3, 4, 5, 4, 5, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 5, 4, 5, 3, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
lambda(n) is the Carmichael lambda function, A002322.
a(n) = (length of row n in table A246700) - 1. - Reinhard Zumkeller, Sep 02 2014
LINKS
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 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. [Annotated copy with A-numbers]
Paul Erdős, A. Granville, C. Pomerance, and C. Spiro, On the Normal Behavior of the Iterates of some Arithmetic Functions, in Analytic number theory (Allerton Park, IL, 1989), Progr. Math., 85 Birkhäuser Boston, Boston, MA, (1990), 165-204.
Nick Harland, The iterated Carmichael lambda function, arXiv:1111.3667v1 [math.NT], Nov 15, 2011.
Nick Harland, The number of iterates of the Carmichael lambda function required to reach 1, arXiv:1203.4791 [math.NT], Mar 21, 2012.
FORMULA
For n > 1: a(n) = a(A002322(n)) + 1. - Reinhard Zumkeller, Sep 02 2014
EXAMPLE
If n = 23 the trajectory is 23, 22, 10, 4, 2, 1. Its length is 6, thus a(23) = 5.
MAPLE
a:= n-> `if`(n=1, 0, 1+a(numtheory[lambda](n))):
seq(a(n), n=1..100); # Alois P. Heinz, Apr 27 2019
MATHEMATICA
f[n_] := Length[ NestWhileList[ CarmichaelLambda, n, Unequal, 2]] - 2; Table[f[n], {n, 1, 120}]
PROG
(Haskell)
a185816 n = if n == 1 then 0 else a185816 (a002322 n) + 1
-- Reinhard Zumkeller, Sep 02 2014
CROSSREFS
Sequence in context: A350065 A077982 A331921 * A324901 A295568 A099427
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 05 2011
STATUS
approved

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