%I #12 Dec 28 2017 07:55:47
%S 1,1,2,5,11,33,92,347,1347,6338,31949,179265,1071264,6845487,46162569,
%T 327731596,2437753739,18948597836,153498350744,1293123237572,
%U 11306475314372,102425554267565,959826755336241,9290811905211847
%N Number of primitive (period n) bracelet structures using an infinite alphabet.
%F a(n) = Sum_{d|n} mu(n/d) * A084708(d).
%t u[0, _] = 1; u[k_, j_] := u[k, j] = Sum[Binomial[k - 1, i - 1] Total[u[k - i, j] #^(i - 1) & /@ Divisors[j]], {i, k}];
%t b[n_] := 1/n*Total[EulerPhi[#] u[Quotient[n, #], #]& /@ Divisors[n] ];
%t A084708[n_] := b[n]/2 + If[EvenQ[n], u[n/2, 2], Sum[Binomial[n/2 - 1/2, k] u[k, 2], {k, 0, n/2 - 1/2}]]/2;
%t a[n_] := Sum[MoebiusMu[n/d]*A084708[d], {d, Divisors[n]}];
%t Array[a, 24] (* _Jean-François Alcover_, Dec 28 2017, after _Andrew Howroyd_ and _Wouter Meeussen_ *)
%Y Row sums of A276543.
%Y Cf. A084708.
%K nonn
%O 1,3
%A _Andrew Howroyd_, Apr 09 2017