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

Offset: 1

Author

Valery A. Liskovets, Jan 17 2006

Keywords

• easy
• nonn

Comments

a(p)=1 for prime p.

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

Programs

Mathematica

A053656[n_] := Total[EulerPhi[#] 2^(n/#)& /@ Divisors[n]]/(2n) + 2^(n/2-2)* (1 - Mod[n, 2]);
A066313[n_] := DivisorSum[n, A053656[#] MoebiusMu[n/#]&];
a[n_] := A053656[n] - A066313[n];
Array[a, 35] (* Jean-François Alcover, Aug 28 2019 *)

Formula

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

Extensions

More terms from Jean-François Alcover, Aug 28 2019