A343565 a(n) = |{(x_1, x_2, ... , x_n) : 1 <= x_1 <= x_2 <= ... <= x_n <= n, gcd(x_1, x_2, ... , x_n, n) = 1}|.

1, 2, 9, 30, 125, 428, 1715, 6270, 24255, 91367, 352715, 1345448, 5200299, 20019526, 77554749, 300295038, 1166803109, 4535971916, 17672631899, 68913247655, 269128640958, 1051984969598, 4116715363799, 16123381989000, 63205303195125, 247956558998878, 973469689288236

Offset

1,2

Links

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

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[n/#] * Binomial[# + n - 1, n] &]; Array[a, 30] (* Amiram Eldar, Apr 25 2021 *)

Prog

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

Crossrefs

Cf. A000010, A007438, A117108, A117109, A332470, A343517, A343548, A343549.

Sequence in context: A234007 A203365 A181954 * A318101 A358652 A347893

Adjacent sequences: A343562 A343563 A343564 * A343566 A343567 A343568

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2021

Status

approved