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%I #11 Aug 28 2019 08:15:17
%S 0,0,1,1,2,1,4,1,8,3,17,1,56,1,134,18,440,1,1434,1,4758,135,16160,1,
%T 57254,16,200475,1387,718152,1,2591800,1,9398520,16161,34324175,148,
%U 126125330,1,465093572,200476,1723176740,1,6408642359,1,23910576236,2588402,89494164974,1,335923316982,133,1264107421202
%N Number of imprimitive (periodic) 2n-bead black-white reversible necklaces with n black beads.
%C a(p)=1 for prime p.
%F a(n) = A005648(n) - A045628(n).
%t A005648[0] = 1; A005648[n_] := (1/2)(Binomial[2 Quotient[n, 2], Quotient[n, 2]] + DivisorSum[n, EulerPhi[#] Binomial[2n/#, n/#] &]/(2n));
%t A045628[n_] := If[n == 0, 1, Sum[MoebiusMu[n/d] (2n Binomial[2 Quotient[d, 2], Quotient[d, 2]] + Binomial[2d, d]), {d, Divisors[n]}]/(4n)];
%t a[n_] := A005648[n] - A045628[n];
%t Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Aug 28 2019 *)
%K easy,nonn
%O 0,5
%A _Valery A. Liskovets_, Jan 17 2006
%E More terms from _Jean-François Alcover_, Aug 28 2019
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