The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054628 Number of n-bead necklaces with 9 colors. 2
 1, 9, 45, 249, 1665, 11817, 88725, 683289, 5381685, 43046889, 348684381, 2852823609, 23535840225, 195528140649, 1634056945605, 13726075481049, 115813764494505, 981010688215689, 8338590871415805, 71097458824894329, 607883273127192897 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Eric Weisstein's World of Mathematics, Necklace. FORMULA a(n) = (1/n)*Sum_{d|n} phi(d)*9^(n/d), n > 0. G.f.: 1 - Sum_{n>=1} phi(n)*log(1 - 9*x^n)/n. - Herbert Kociemba, Nov 02 2016 [corrected by Ilya Gutkovskiy, Apr 17 2021] a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} 9^gcd(n,k). - Ilya Gutkovskiy, Apr 17 2021 EXAMPLE G.f. = 1 + 9*x + 45*x^2 + 249*x^3 + 1665*x^4 + 11817*x^5 + 88725*x^6 + ... MAPLE with(combstruct):A:=[N, {N=Cycle(Union(Z\$9))}, unlabeled]: seq(count(A, size=n), n=0..20); # Zerinvary Lajos, Dec 05 2007 MATHEMATICA mx=40; CoefficientList[Series[1-Sum[EulerPhi[i] Log[1-9*x^i]/i, {i, 1, mx}], {x, 0, mx}], x] (* Herbert Kociemba, Nov 02 2016 *) k=9; 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)*9^(n/d))); \\ Altug Alkan, Sep 21 2018 CROSSREFS Column 9 of A075195. Cf. A054616. Sequence in context: A270567 A316108 A026092 * A132133 A009410 A290358 Adjacent sequences:  A054625 A054626 A054627 * A054629 A054630 A054631 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)