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A115122 Number of imprimitive (periodic) 2n-bead black-white complementable necklaces with n black beads. 0
0, 0, 1, 1, 2, 1, 4, 1, 7, 3, 16, 1, 49, 1, 129, 17, 415, 1, 1408, 1, 4659, 130, 16081, 1, 56858, 15, 200171, 1367, 716733, 1, 2590529, 1, 9393119, 16082, 34319668, 142, 126104312, 1, 465076161, 200172, 1723097474, 1, 6408573532, 1, 23910271229, 2587214, 89493903439 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(p)=1 for prime p.

LINKS

Table of n, a(n) for n=0..46.

FORMULA

a(n)=A045629(n) - A045632(n).

MATHEMATICA

A045629[n_] := If[n==0, 1, (1/(2n)) DivisorSum[n, EulerPhi[n/#] Binomial[ 2 # - 1, # - 1] + EulerPhi[2 (n/#)] 2^(# - 1)&]];

A045632[n_] := If[n==0, 1, Sum[MoebiusMu[n/d] A045629[d], {d, Divisors[n]}]];

a[n_] := A045629[n] - A045632[n];

Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Aug 28 2019 *)

CROSSREFS

Sequence in context: A252751 A199744 A115124 * A097360 A325348 A307683

Adjacent sequences:  A115119 A115120 A115121 * A115123 A115124 A115125

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 September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)