A115122 Number of imprimitive (periodic) 2n-bead black-white complementable necklaces with n black beads.

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

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: A199744 A360870 A115124 * A097360 A360862 A325348

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