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.
%I A054629 #30 Feb 16 2025 08:32:42
%S A054629 1,10,55,340,2530,20008,166870,1428580,12501280,111111340,1000010044,
%T A054629 9090909100,83333418520,769230769240,7142857857190,66666666680272,
%U A054629 625000006251280,5882352941176480,55555555611222370,526315789473684220
%N A054629 Number of n-bead necklaces with 10 colors.
%H A054629 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Necklace.html">Necklace.</a>
%H A054629 <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>
%F A054629 a(n) = (1/n)*Sum_{d|n} phi(d)*10^(n/d) = A054617(n)/n, n > 0.
%F A054629 G.f.: 1 - Sum_{n>=1} phi(n)*log(1 - 10*x^n)/n. - _Herbert Kociemba_, Nov 02 2016
%F A054629 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} 10^gcd(n,k). - _Ilya Gutkovskiy_, Apr 17 2021
%e A054629 G.f. = 1 + 10*x + 55*x^2 + 340*x^3 + 2530*x^4 + 20008*x^5 + 166870*x^6 + ...
%p A054629 with(combstruct):A:=[N,{N=Cycle(Union(Z$10))},unlabeled]: seq(count(A,size=n),n=0..19); # _Zerinvary Lajos_, Dec 05 2007
%t A054629 mx=40; CoefficientList[Series[1-Sum[EulerPhi[i] Log[1-10*x^i]/i, {i, 1, mx}], {x, 0, mx}], x] (* _Herbert Kociemba_, Nov 02 2016 *)
%t A054629 k=10; Prepend[Table[DivisorSum[n, EulerPhi[#] k^(n/#) &]/n, {n, 1, 30}], 1] (* _Robert A. Russell_, Sep 21 2018 *)
%o A054629 (PARI) a(n)=if(n==0, 1, 1/n*sumdiv(n, d, eulerphi(d)*10^(n/d))); \\ _Altug Alkan_, Sep 21 2018
%Y A054629 Column 10 of A075195.
%Y A054629 Cf. A054617.
%K A054629 nonn
%O A054629 0,2
%A A054629 _N. J. A. Sloane_, Apr 16 2000
%E A054629 Edited by _Christian G. Bower_, Sep 07 2002
%E A054629 a(0) corrected by _Herbert Kociemba_, Nov 02 2016