login
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, 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
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
KEYWORD
nonn
AUTHOR
Miles Englezou, Dec 15 2023
STATUS
approved