login
A276547
Number of primitive (period n) n-bead necklace structures using an infinite alphabet.
3
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
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 09 2017
STATUS
approved