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

1,4

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]);
A066313[n_] := DivisorSum[n, A053656[#] MoebiusMu[n/#]&];
a[n_] := A053656[n] - A066313[n];
Array[a, 35] (* Jean-François Alcover, Aug 28 2019 *)

Crossrefs

Sequence in context: A358195 A143862 A115118 * A323523 A371092 A124072

Adjacent sequences: A115118 A115119 A115120 * A115122 A115123 A115124

Keyword

easy,nonn

Author

Valery A. Liskovets, Jan 17 2006

Extensions

More terms from Jean-François Alcover, Aug 28 2019

Status

approved