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A115119 Number of imprimitive (periodic) n-bead necklaces with beads of 2 colors when turning over is allowed. 0
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, 46, 690, 2, 1302, 2, 2250, 128, 4113, 24, 7896, 2, 14311, 382, 27036, 2, 51641, 2, 96912, 1266, 184411, 2, 354918, 18, 675258, 4114, 1296861, 2, 2501365, 132, 4806102, 14312 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(p)=2 for prime p.

LINKS

Table of n, a(n) for n=0..57.

FORMULA

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

MATHEMATICA

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);

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

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

Array[a, 70, 0] (* Jean-François Alcover, Aug 28 2019 *)

CROSSREFS

Cf. A000029, A001371.

Sequence in context: A322366 A164941 A328673 * A066656 A164896 A298422

Adjacent sequences:  A115116 A115117 A115118 * A115120 A115121 A115122

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Jan 17 2006

EXTENSIONS

More terms from Jean-François Alcover, Aug 28 2019

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)