A345131 Number of ordered n-tuples of integers from [ 1..n ] with no global factor.

1, 2, 8, 29, 118, 427, 1671, 6260, 24034, 91301, 351261, 1345434, 5191170, 20018845, 77500485, 300290041, 1166450850, 4535971707, 17670369300, 68913194733, 269114332057, 1051984590581, 4116622325140, 16123381985750, 63204699026898, 247956554702702

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{k=1..n} Sum_{d|k} mu(k/d) * binomial(d+n-2, d-1).

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - x^k)^n.

a(n) ~ 2^(2*n-1) / sqrt(Pi*n). - Vaclav Kotesovec, Jun 19 2021

Mathematica

a[n_] := Sum[DivisorSum[k, MoebiusMu[k/#] * Binomial[n + # - 2, # - 1] &], {k, 1, n}]; Array[a, 25] (* Amiram Eldar, Jun 13 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, sumdiv(k, d, moebius(k/d)*binomial(d+n-2, d-1)));

Crossrefs

Main diagonal of A177976.

Cf. A332470.

Sequence in context: A011367 A220547 A261774 * A150733 A150734 A150735

Adjacent sequences: A345128 A345129 A345130 * A345132 A345133 A345134

Keyword

nonn

Author

Seiichi Manyama, Jun 12 2021

Status

approved