A066313 -id:A066313 - cp's OEIS frontend

A066314 Number of identity (asymmetric) bracelets (or necklaces) with n red or blue beads such that the beads switch colors when bracelet is turned over.

1, 0, 1, 1, 3, 3, 9, 12, 28, 42, 93, 154, 315, 549, 1091, 1980, 3855, 7140, 13797, 25941, 49929, 94767, 182361, 348430, 671088, 1288350, 2485504, 4789134, 9256395, 17886951, 34636833, 67091520, 130150493, 252610440, 490853403

Offset: 1

Christian G. Bower, Dec 13 2001

nonn

Index entries for sequences related to bracelets

a(n)=A001037(n)-A066313(n).

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.

Original entry on oeis.org

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

Valery A. Liskovets, Jan 17 2006

a(p)=1 for prime p.

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

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 *)

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

More terms from Jean-François Alcover, Aug 28 2019

cp's OEIS Frontend

A066314 Number of identity (asymmetric) bracelets (or necklaces) with n red or blue beads such that the beads switch colors when bracelet is turned over.

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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.

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