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

1,11

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.

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A320105 A120698 A338411 * A326775 A349410 A317240

Adjacent sequences: A366776 A366777 A366778 * A366780 A366781 A366782

Keyword

nonn

Author

Miles Englezou, Dec 15 2023

Status

approved