%I #20 Feb 03 2022 13:52:39
%S 3,1,2,3,6,9,18,30,56,99,186,335,630,1161,2182,4080,7710,14532,27594,
%T 52377,99858,190557,364722,698870,1342176,2580795,4971008,9586395,
%U 18512790,35790267,69273666,134215680,260300986,505286415,981706806,1908866960,3714566310
%N Number of orbits of length n in map whose periodic points are A000051.
%H Y. Puri and T. Ward, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL4/WARD/short.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
%H Yash Puri and Thomas Ward, <a href="http://www.fq.math.ca/Scanned/39-5/puri.pdf">A dynamical property unique to the Lucas sequence</a>, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402.
%F a(n) = (1/n)* Sum_{d|n} mu(d)*A000051(n/d).
%e a(3)=2 since the 3rd term of A000051 is 9 and the first term is 3.
%o (PARI) a000051(n) = 2^n+1;
%o a(n) = (1/n)*sumdiv(n, d, moebius(d)*a000051(n/d)); \\ _Michel Marcus_, Sep 11 2017
%o (Python)
%o from sympy import mobius, divisors
%o 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
%Y Cf. A000051.
%Y Cf. A001037, A059966 (both nearly identical to this sequence).
%Y Cf. A093210.
%K easy,nonn
%O 1,1
%A _Thomas Ward_
%E A048578 replaced by A000051 in name and formula by _Michel Marcus_, Sep 11 2017