A181776 a(n) = lambda(lambda(n)), where lambda(n) is the Carmichael lambda function (A002322).

1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 4, 1, 2, 2, 2, 2, 4, 2, 6, 2, 2, 4, 10, 1, 4, 2, 6, 2, 6, 2, 4, 2, 4, 4, 2, 2, 6, 6, 2, 2, 4, 2, 6, 4, 2, 10, 22, 2, 6, 4, 4, 2, 12, 6, 4, 2, 6, 6, 28, 2, 4, 4, 2, 4, 2, 4, 10, 4, 10, 2, 12, 2, 6, 6, 4, 6, 4, 2, 12, 2, 18, 4, 40, 2, 4, 6, 6

Offset: 1

Author

Michel Lagneau, Nov 12 2010

Keywords

• nonn

Comments

Harland proves the conjecture of Martin & Pomerance that a(n) = n exp ((1 + o(1))(log log n)^2 log log log n) for almost all n, as well as a generalization to k-th iterates. - Charles R Greathouse IV, Dec 21 2011

Examples

			a(11) = 4 is in the sequence because A002322(11) = 10 and A002322(10) = 4.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Nick Harland, The iterated Carmichael lambda function, arXiv:1111.3667 [math.NT], 2011.
• G. Martin and C. Pomerance, The iterated Carmichael lambda-function and the number of cycles of the power generator, Acta Arith. 118:4 (2005), pp. 305-335.

Crossrefs

Cf. A002322, A002997.

Programs

Mathematica

Table[CarmichaelLambda[CarmichaelLambda[n]],{n,1,100}]
Table[Nest[CarmichaelLambda,n,2],{n,100}] (* Harvey P. Dale, Jul 01 2020 *)

PARI

a(n)=lcm(znstar(lcm(znstar(n)[2]))[2]) \\ Charles R Greathouse IV, Nov 04 2012