cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A032165 Number of aperiodic necklaces of n beads of 10 colors.

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%I A032165 #32 May 19 2019 13:08:05
%S A032165 10,45,330,2475,19998,166485,1428570,12498750,111111000,999989991,
%T A032165 9090909090,83333249175,769230769230,7142856428565,66666666659934,
%U A032165 624999993750000,5882352941176470,55555555499944500
%N A032165 Number of aperiodic necklaces of n beads of 10 colors.
%H A032165 Vincenzo Librandi, <a href="/A032165/b032165.txt">Table of n, a(n) for n = 1..500</a>
%H A032165 C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H A032165 Y. Puri and T. Ward, <a href="http://www.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 A032165 F. Ruskey, <a href="http://combos.org/necklace">Necklaces, Lyndon words, De Bruijn sequences, etc.</a>
%H A032165 F. Ruskey, <a href="/A000011/a000011.pdf">Necklaces, Lyndon words, De Bruijn sequences, etc.</a> [Cached copy, with permission, pdf format only]
%H A032165 <a href="/index/Lu#Lyndon">Index entries for sequences related to Lyndon words</a>
%F A032165 "CHK" (necklace, identity, unlabeled) transform of 10, 0, 0, 0...
%F A032165 a(n) = Sum_{d|n} mu(d)*10^(n/d)/n.
%F A032165 G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 10*x^k))/k. - _Ilya Gutkovskiy_, May 19 2019
%t A032165 f[d_]:=MoebiusMu[d] 10^(n/d)/n; a[n_]:=Total[f/@Divisors[n]]; a[0]=1; Table[a[n], {n, 1, 20}] (* _Vincenzo Librandi_, Oct 14 2017 *)
%o A032165 (PARI) a(n) = sumdiv(n, d, moebius(d)*10^(n/d))/n; \\ _Andrew Howroyd_, Oct 13 2017
%Y A032165 Column 10 of A074650.
%K A032165 nonn
%O A032165 1,1
%A A032165 _Christian G. Bower_