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 A278641 #16 Sep 25 2018 17:58:38
%S A278641 0,0,0,10,45,252,1130,5270,23520,106960,483756,2211650,10149805,
%T A278641 46911060,217868310,1017057518,4767797895,22438419120,105960938380,
%U A278641 501928967930,2384171386941,11353241261180,54185968572450,259150507387910,1241763071712930,5960463867187752,28656077411358180,137973711706163210
%N A278641 Number of pairs of orientable necklaces with n beads and up to 5 colors; i.e., turning the necklace over does not leave it unchanged. The turned-over necklace is not included in the count.
%C A278641 Number of chiral bracelets of n beads using up to five different colors.
%F A278641 G.f.: k=5, (1 - Sum_{n>=1} phi(n)*log(1 - k*x^n)/n - Sum_{i=0..2} Binomial[k,i]*x^i / ( 1-k*x^2) )/2.
%F A278641 For n>0, a(n) = -(k^floor((n+1)/2) + k^ceiling((n+1)/2))/4 + (1/2n)* Sum_{d|n} phi(d)*k^(n/d), where k=5 is the maximum number of colors. - _Robert A. Russell_, Sep 24 2018
%t A278641 mx=40;f[x_,k_]:=(1-Sum[EulerPhi[n]*Log[1-k*x^n]/n,{n,1,mx}]-Sum[Binomial[k,i]*x^i,{i,0,2}]/(1-k*x^2))/2;CoefficientList[Series[f[x,5],{x,0,mx}],x]
%t A278641 k=5; Prepend[Table[DivisorSum[n, EulerPhi[#] k^(n/#) &]/(2n) - (k^Floor[(n+1)/2] + k^Ceiling[(n+1)/2])/4, {n, 1, 30}], 0] (* _Robert A. Russell_, Sep 24 2018 *)
%Y A278641 Column 5 of A293496.
%Y A278641 Cf. A059076 (2 colors), A278639 (3 colors), A278640 (4 colors).
%Y A278641 a(n) = (A001869(n) - A056487(n+1)) / 2 = A032276(n) - A056487(n+1).
%Y A278641 Equals A001869 - A032276.
%K A278641 nonn
%O A278641 0,4
%A A278641 _Herbert Kociemba_, Nov 24 2016