A366779 a(n) = lambda(lambda(lambda(n))), where lambda(n) is the Carmichael lambda function (A002322).

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, 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, 4, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 6, 2, 4, 1, 2, 2, 2

Offset: 1

Author

Miles Englezou, Dec 15 2023

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000
• N. 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 (lambda function), A181776 (lambda function at two iterations).

Programs

Maple

a:= n-> (numtheory[lambda]@@3)(n):
seq(a(n), n=1..100);  # Alois P. Heinz, Jan 19 2024

Mathematica

a[n_]:=Nest[CarmichaelLambda,n,3]; Array[a,87] (* Stefano Spezia, Jan 20 2024 *)

PARI

a(n) = lcm(znstar(lcm(znstar(lcm(znstar(11)[2]))[2]))[2])

Python

from sympy import reduced_totient
def A366779(n): return reduced_totient(reduced_totient(reduced_totient(n))) # Chai Wah Wu, Jan 29 2024

Formula

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