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 A345131 Number of ordered n-tuples of integers from [ 1..n ] with no global factor. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 17 03:10 EDT 2024. Contains 375984 sequences. (Running on oeis4.)