cp's OEIS Frontend

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

%I A181776 #23 Jul 01 2020 20:00:00
%S A181776 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,
%T A181776 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,
%U A181776 10,4,10,2,12,2,6,6,4,6,4,2,12,2,18,4,40,2,4,6,6
%N A181776 a(n) = lambda(lambda(n)), where lambda(n) is the Carmichael lambda function (A002322).
%C A181776 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
%H A181776 Charles R Greathouse IV, <a href="/A181776/b181776.txt">Table of n, a(n) for n = 1..10000</a>
%H A181776 Nick Harland, <a href="https://arxiv.org/abs/1111.3667">The iterated Carmichael lambda function</a>, arXiv:1111.3667 [math.NT], 2011.
%H A181776 G. Martin and C. Pomerance, <a href="http://www.math.dartmouth.edu/~carlp/PDF/lambda030205.pdf">The iterated Carmichael lambda-function and the number of cycles of the power generator</a>, Acta Arith. 118:4 (2005), pp. 305-335.
%e A181776 a(11) = 4 is in the sequence because A002322(11) = 10 and A002322(10) = 4.
%t A181776 Table[CarmichaelLambda[CarmichaelLambda[n]],{n,1,100}]
%t A181776 Table[Nest[CarmichaelLambda,n,2],{n,100}] (* _Harvey P. Dale_, Jul 01 2020 *)
%o A181776 (PARI) a(n)=lcm(znstar(lcm(znstar(n)[2]))[2]) \\ _Charles R Greathouse IV_, Nov 04 2012
%Y A181776 Cf. A002322, A002997.
%K A181776 nonn
%O A181776 1,5
%A A181776 _Michel Lagneau_, Nov 12 2010