A115119 - OEIS

%I #9 Aug 28 2019 08:15:11

%S 0,0,2,2,3,2,5,2,6,4,9,2,16,2,19,10,30,2,55,2,81,20,127,2,248,8,381,

%T 46,690,2,1302,2,2250,128,4113,24,7896,2,14311,382,27036,2,51641,2,

%U 96912,1266,184411,2,354918,18,675258,4114,1296861,2,2501365,132,4806102,14312

%N Number of imprimitive (periodic) n-bead necklaces with beads of 2 colors when turning over is allowed.

%C a(p)=2 for prime p.

%F a(n) = A000029(n) - A001371(n).

%t a29[n_] := a29[n] = (s = If[OddQ[n], 2^((n-1)/2), 2^(n/2-2) + 2^(n/2 - 1)]; a29[0] = 1; Do[s = s + EulerPhi[d] 2^(n/d)/(2n), {d, Divisors[n]}]; s);

%t a1371[n_] := Sum[MoebiusMu[d] a29[n/d], {d, Divisors[n]}]; a1371[0] = 1;

%t a[0] = 0; a[n_] := a29[n] - a1371[n];

%t Array[a, 70, 0] (* _Jean-François Alcover_, Aug 28 2019 *)

%Y Cf. A000029, A001371.

%K easy,nonn

%O 0,3

%A _Valery A. Liskovets_, Jan 17 2006

%E More terms from _Jean-François Alcover_, Aug 28 2019