A276547 - OEIS

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

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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 *)