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 A054626 #31 Feb 16 2025 08:32:42
%S A054626 1,7,28,119,616,3367,19684,117655,720916,4483815,28249228,179756983,
%T A054626 1153450872,7453000807,48444564052,316504102999,2077058521216,
%U A054626 13684147881607,90467424361132,599941851861751,3989613329006536,26597422099282535
%N A054626 Number of n-bead necklaces with 7 colors.
%H A054626 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Necklace.html">Necklace.</a>
%H A054626 <a href="/index/Ne#necklaces">Index entries for sequences related to necklaces</a>
%F A054626 a(n) = (1/n)*Sum_{d|n} phi(d)*7^(n/d), n > 0.
%F A054626 G.f.: 1 - Sum_{n>=1} phi(n)*log(1 - 7*x^n)/n. - _Herbert Kociemba_, Nov 02 2016
%F A054626 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} 7^gcd(n,k). - _Ilya Gutkovskiy_, Apr 17 2021
%e A054626 G.f. = 1 + 7*x + 28*x^2 + 119*x^3 + 616*x^4 + 3367*x^5 + 19684*x^6 + ...
%p A054626 with(combstruct):A:=[N,{N=Cycle(Union(Z$7))},unlabeled]: seq(count(A,size=n),n=0..21); # _Zerinvary Lajos_, Dec 05 2007
%t A054626 mx=40; CoefficientList[Series[1-Sum[EulerPhi[i] Log[1-7*x^i]/i, {i, 1, mx}], {x, 0, mx}], x] (* _Herbert Kociemba_, Nov 02 2016 *)
%t A054626 k=7; Prepend[Table[DivisorSum[n, EulerPhi[#] k^(n/#) &]/n, {n, 1, 30}], 1] (* _Robert A. Russell_, Sep 21 2018 *)
%o A054626 (PARI) a(n)=if(n==0, 1, 1/n*sumdiv(n, d, eulerphi(d)*7^(n/d))); \\ _Altug Alkan_, Sep 21 2018
%Y A054626 Column 7 of A075195.
%Y A054626 Cf. A054614.
%K A054626 nonn
%O A054626 0,2
%A A054626 _N. J. A. Sloane_, Apr 16 2000
%E A054626 Edited by _Christian G. Bower_, Sep 07 2002
%E A054626 a(0) corrected by _Herbert Kociemba_, Nov 02 2016