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

Author

Andrew Howroyd, Apr 09 2017

Keywords

• nonn

Links

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

Crossrefs

Row sums of A107424.

Cf. A084423.

Programs

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 *)

Formula

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