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 A306669 #9 Aug 19 2019 16:26:14
%S A306669 1,0,1,4,23,110,719,4992,40302,362492,3628799,39912804,479001599,
%T A306669 6226974714,87178289207,1307673722880,20922789887999,355687417744992,
%U A306669 6402373705727999,121645100223036700,2432902008176115023,51090942167993548790,1124000727777607679999
%N A306669 Number of aperiodic permutation necklaces of weight n.
%C A306669 A permutation is aperiodic if every rotation of {1...n} acts on the vertices of the cycle decomposition to produce a different digraph. A permutation necklace is an equivalence class of permutations under the action of rotation of vertices in the cycle decomposition. The corresponding action on words applies m -> m + 1 for m < n and n -> 1, and rotates once to the right. For example, (24531) first becomes (35142) under the application of cyclic rotation, and then is rotated right to give (23514).
%H A306669 Andrew Howroyd, <a href="/A306669/b306669.txt">Table of n, a(n) for n = 1..200</a>
%H A306669 Gus Wiseman, <a href="/A306669/a306669.png">Inequivalent representatives of the a(5) = 23 aperiodic necklace permutations</a>.
%F A306669 a(n) = A324514(n)/n.
%F A306669 a(n) = (1/n)*Sum_{d|n} mu(n/d)*(n/d)^d*d!. - _Andrew Howroyd_, Aug 19 2019
%t A306669 Table[Length[Select[Permutations[Range[n]],UnsameQ@@NestList[RotateRight[#/.k_Integer:>If[k==n,1,k+1]]&,#,n-1]&]]/n,{n,6}]
%o A306669 (PARI) a(n) = (1/n)*sumdiv(n, d, moebius(n/d)*(n/d)^d*d!); \\ _Andrew Howroyd_, Aug 19 2019
%Y A306669 Cf. A000031, A000740, A000939, A001037, A059966, A060223, A061417, A086675, A323861, A323865, A323866, A323871.
%Y A306669 Cf. A324461, A324512, A324513, A324514.
%K A306669 nonn
%O A306669 1,4
%A A306669 _Gus Wiseman_, Mar 04 2019
%E A306669 Terms a(10) and beyond from _Andrew Howroyd_, Aug 19 2019