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A060477
Number of orbits of length n in map whose periodic points are A000051.
4
3, 1, 2, 3, 6, 9, 18, 30, 56, 99, 186, 335, 630, 1161, 2182, 4080, 7710, 14532, 27594, 52377, 99858, 190557, 364722, 698870, 1342176, 2580795, 4971008, 9586395, 18512790, 35790267, 69273666, 134215680, 260300986, 505286415, 981706806, 1908866960, 3714566310
OFFSET
1,1
LINKS
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402.
FORMULA
a(n) = (1/n)* Sum_{d|n} mu(d)*A000051(n/d).
EXAMPLE
a(3)=2 since the 3rd term of A000051 is 9 and the first term is 3.
PROG
(PARI) a000051(n) = 2^n+1;
a(n) = (1/n)*sumdiv(n, d, moebius(d)*a000051(n/d)); \\ Michel Marcus, Sep 11 2017
(Python)
from sympy import mobius, divisors
def A060477(n): return sum(mobius(n//d)*(2**d+1) for d in divisors(n, generator=True))//n # Chai Wah Wu, Feb 03 2022
CROSSREFS
Cf. A000051.
Cf. A001037, A059966 (both nearly identical to this sequence).
Cf. A093210.
Sequence in context: A078350 A078719 A087227 * A345037 A175945 A209859
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
A048578 replaced by A000051 in name and formula by Michel Marcus, Sep 11 2017
STATUS
approved