A276547 Number of primitive (period n) n-bead necklace structures using an infinite alphabet.

1, 1, 2, 5, 11, 39, 126, 537, 2358, 11690, 61689, 351725, 2126496, 13639244, 92197509, 655035225, 4874404107, 37893368072, 306986431846, 2586209738004, 22612848403442, 204850732418594, 1919652428481929, 18581619724011091, 185543613289200937, 1908894098864372104

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Formula

a(n) = Sum_{d|n} mu(n/d) * A084423(d).

Mathematica

u[0, _] = 1; u[k_, j_] := u[k, j] = Sum[Binomial[k - 1, i - 1]*DivisorSum[j, u[k - i, j]*#^(i - 1)&], {i, 1, k}];
b[0] = 1; b[n_] := DivisorSum[n, EulerPhi[#]*u[n/#, #]&]/n;
a[1] = 1; a[n_] := DivisorSum[n, MoebiusMu[n/#]*b[#]&];
Array[a, 26] (* Jean-François Alcover, Jun 16 2017, using Franklin T. Adams-Watters' code for A084423 *)

Crossrefs

Row sums of A107424.

Cf. A084423.

Sequence in context: A056301 A001344 A056302 * A065850 A191029 A106886

Adjacent sequences: A276544 A276545 A276546 * A276548 A276549 A276550

Keyword

nonn

Author

Andrew Howroyd, Apr 09 2017

Status

approved