OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Necklace.
FORMULA
a(n) = (1/n)*Sum_{d|n} phi(d)*8^(n/d), n > 0.
G.f.: 1 - Sum_{n>=1} phi(n)*log(1 - 8*x^n)/n. - Herbert Kociemba, Nov 02 2016
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} 8^gcd(n,k). - Ilya Gutkovskiy, Apr 17 2021
EXAMPLE
G.f. = 1 + 8*x + 36*x^2 + 176*x^3 + 1044*x^4 + 6560*x^5 + 43800*x^6 + ...
MAPLE
with(combstruct):A:=[N, {N=Cycle(Union(Z$8))}, unlabeled]: seq(count(A, size=n), n=0..20); # Zerinvary Lajos, Dec 05 2007
MATHEMATICA
mx=40; CoefficientList[Series[1-Sum[EulerPhi[i] Log[1-8*x^i]/i, {i, 1, mx}], {x, 0, mx}], x] (* Herbert Kociemba, Nov 02 2016 *)
k=8; Prepend[Table[DivisorSum[n, EulerPhi[#] k^(n/#) &]/n, {n, 1, 30}], 1] (* Robert A. Russell, Sep 21 2018 *)
PROG
(PARI) a(n)=if(n==0, 1, 1/n*sumdiv(n, d, eulerphi(d)*8^(n/d))); \\ Altug Alkan, Sep 21 2018
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