A115121 - OEIS

A115121

Number of imprimitive (periodic) bracelets (or necklaces) with n red or blue beads such that the beads switch colors when bracelet is turned over.

0, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 11, 1, 11, 5, 22, 1, 37, 1, 64, 11, 95, 1, 210, 4, 317, 30, 625, 1, 1160, 1, 2122, 95, 3857, 13, 7612, 1, 13799, 317, 26518, 1, 50559, 1, 95887, 1124, 182363, 1, 352750, 10, 671150, 3857, 1292764, 1, 2492933, 97, 4797904, 13799

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OFFSET

1,4

COMMENTS

a(p)=1 for prime p.

Presumably a(n) = A115118(n) = A066656(n)/2 for odd n.

LINKS

Table of n, a(n) for n=1..57.

FORMULA

a(n) = A053656(n) - A066313(n).

MATHEMATICA

A053656[n_] := Total[EulerPhi[#] 2^(n/#)& /@ Divisors[n]]/(2n) + 2^(n/2-2)* (1 - Mod[n, 2]);