A185816 Number of iterations of lambda(n) needed to reach 1.
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
Offset: 1
Keywords
Examples
If n = 23 the trajectory is 23, 22, 10, 4, 2, 1. Its length is 6, thus a(23) = 5.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
- 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.
Programs
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Haskell
a185816 n = if n == 1 then 0 else a185816 (a002322 n) + 1 -- Reinhard Zumkeller, Sep 02 2014
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Maple
a:= n-> `if`(n=1, 0, 1+a(numtheory[lambda](n))): seq(a(n), n=1..100); # Alois P. Heinz, Apr 27 2019
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Mathematica
f[n_] := Length[ NestWhileList[ CarmichaelLambda, n, Unequal, 2]] - 2; Table[f[n], {n, 1, 120}]
Formula
For n > 1: a(n) = a(A002322(n)) + 1. - Reinhard Zumkeller, Sep 02 2014
Comments