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

Author

Seiichi Manyama, Jun 12 2021

Keywords

• nonn

Links

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

Crossrefs

Main diagonal of A177976.

Cf. A332470.

Programs

Mathematica

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

PARI

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

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