%I #15 Aug 29 2019 05:26:48

%S 0,0,1,1,2,1,3,1,4,2,5,1,10,1,11,5,20,1,36,1,58,11,95,1,196,4,317,30,

%T 598,1,1153,1,2068,95,3857,13,7488,1,13799,317,26288,1,50531,1,95422,

%U 1124,182363,1,351764,10,671144,3857,1290874,1,2492820,97,4794104,13799,9256397,1,17923218,1,34636835,49968,67110932,319

%N Number of imprimitive (periodic) n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed.

%C a(p) = 1 for prime p. Presumably a(n) = A115121(n) = A066656(n)/2 for odd n.

%H Antti Karttunen, <a href="/A115118/b115118.txt">Table of n, a(n) for n = 0..1024</a>

%F a(n) = A000013(n) - A000048(n).

%t a[n_] := If[n == 0, 0, Sum[EulerPhi[2d] 2^(n/d) - Boole[OddQ[d]] MoebiusMu[d] 2^(n/d), {d, Divisors[n]}]/(2n)];

%t Array[a, 66, 0] (* _Jean-François Alcover_, Aug 29 2019 *)

%o (PARI) a(n) = if (n==0, 0, (sumdiv(n, d, eulerphi(2*d) * 2^(n/d)) - sumdiv(n, d, (d%2)*(moebius(d)*2^(n/d))))/(2*n)); \\ _Michel Marcus_, Oct 21 2017

%Y Cf. A000013, A000048.

%Y Cf. A115121, A066656.

%K easy,nonn

%O 0,5

%A _Valery A. Liskovets_, Jan 17 2006

%E More terms from _Antti Karttunen_, Oct 21 2017