A366779 - OEIS

%I #24 Feb 05 2024 18:23:55

%S 1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,2,4,1,2,1,2,1,2,1,2,1,2,2,

%T 1,1,2,2,1,1,2,1,2,2,1,4,10,1,2,2,2,1,2,2,2,1,2,2,6,1,2,2,1,2,1,2,4,2,

%U 4,1,2,1,2,2,2,2,2,1,2,1,6,2,4,1,2,2,2

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

%H Alois P. Heinz, <a href="/A366779/b366779.txt">Table of n, a(n) for n = 1..20000</a>

%H N. Harland, <a href="https://arxiv.org/abs/1111.3667">The iterated Carmichael lambda function</a>, arXiv:1111.3667 [math.NT], 2011.

%H 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.

%F a(n) = A002322(A181776(n)).

%e a(5) = 1, since A181776(5) = 2, and A002322(2) = 1.

%p a:= n-> (numtheory[lambda]@@3)(n):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Jan 19 2024

%t a[n_]:=Nest[CarmichaelLambda,n,3]; Array[a,87] (* _Stefano Spezia_, Jan 20 2024 *)

%o (PARI) a(n) = lcm(znstar(lcm(znstar(lcm(znstar(11)[2]))[2]))[2])

%o (Python)

%o from sympy import reduced_totient

%o def A366779(n): return reduced_totient(reduced_totient(reduced_totient(n))) # _Chai Wah Wu_, Jan 29 2024

%Y Cf. A002322 (lambda function), A181776 (lambda function at two iterations).

%K nonn

%O 1,11

%A _Miles Englezou_, Dec 15 2023