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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified May 28 11:40 EDT 2020. Contains 334681 sequences. (Running on oeis4.)