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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.
2
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.
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
KEYWORD
easy,nonn
AUTHOR
Valery A. Liskovets, Jan 17 2006
EXTENSIONS
More terms from Jean-François Alcover, Aug 28 2019
STATUS
approved