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A115123
Number of imprimitive (periodic) bracelets (or necklaces) with n red and blue beads such that the beads switch colors when bracelet is turned over.
0
0, 1, 1, 2, 1, 5, 1, 9, 4, 22, 1, 63, 1, 156, 24, 469, 1, 1532, 1, 4889, 158, 16546, 1, 57844, 21, 202061, 1480, 720533, 1, 2598406, 1, 9408469, 16548, 34350508, 175, 126167112, 1, 465200334, 202063, 1723346534, 1, 6409076632, 1, 23911272097, 2594970, 89495909410, 1
OFFSET
1,4
COMMENTS
a(p)=1 for prime p.
FORMULA
a(n)=A006080(n+1) - A066315(n).
MATHEMATICA
A006080[n_] := Sum[EulerPhi[(n - 1)/k] (Binomial[2k, k]/(2(n - 1))), {k, Divisors[n - 1]}]/2 + 2^(n - 3); A006080[1] = 1;
A066315[n_] := Sum[MoebiusMu[n/d] A006080[d + 1], {d, Divisors[n]}];
a[n_] := A006080[n + 1] - A066315[n];
Array[a, 60] (* Jean-François Alcover, Aug 28 2019 *)
CROSSREFS
Sequence in context: A331888 A178470 A093127 * A132081 A054251 A163963
KEYWORD
easy,nonn
AUTHOR
Valery A. Liskovets, Jan 17 2006
EXTENSIONS
More terms from Jean-François Alcover, Aug 28 2019
STATUS
approved