OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Necklace.
FORMULA
a(n) = (1/n)*Sum_{d|n} phi(d)*6^(n/d), n > 0.
G.f.: 1 - Sum_{n>=1} phi(n)*log(1 - 6*x^n)/n. - Herbert Kociemba, Nov 02 2016
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} 6^gcd(n,k). - Ilya Gutkovskiy, Apr 17 2021
EXAMPLE
G.f. = 1 + 6*x + 21*x^2 + 76*x^3 + 336*x^4 + 1650*x^5 + 7826*x^6 + 39996*x^7 + ...
MAPLE
with(combstruct):A:=[N, {N=Cycle(Union(Z$6))}, unlabeled]: seq(count(A, size=n), n=0..22); # Zerinvary Lajos, Dec 05 2007
MATHEMATICA
f[n_] := Block[{d = Divisors@ n}, Total[EulerPhi[d]*6^(n/d)]/n]; f[0] = 1; Array[f, 23, 0] (* Robert G. Wilson v, Jan 01 2013 *)
mx=40; CoefficientList[Series[1-Sum[EulerPhi[i] Log[1-6*x^i]/i, {i, 1, mx}], {x, 0, mx}], x] (* Herbert Kociemba, Nov 02 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 16 2000
EXTENSIONS
Edited by Christian G. Bower, Sep 07 2002
a(0) corrected by Herbert Kociemba, Nov 02 2016
STATUS
approved