A343517 a(n) = Sum_{1 <= x_1 <= x_2 <= ... <= x_n <= n} gcd(x_1, x_2, ... , x_n, n).

1, 4, 12, 42, 130, 506, 1722, 6622, 24426, 93427, 352726, 1359388, 5200312, 20097156, 77567064, 300787366, 1166803126, 4539197723, 17672631918, 68933307843, 269129530770, 1052113994340, 4116715363822, 16124224571368, 63205303313900, 247961973949536

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..1650

Formula

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

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

a(n) ~ 2^(2*n - 1) / sqrt(Pi*n). - Vaclav Kotesovec, May 23 2021

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#] * Binomial[n + # - 1, n] &]; Array[a, 25] (* Amiram Eldar, Apr 18 2021 *)

Prog

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

Crossrefs

Main diagonal of A343516.

Cf. A000010, A156834, A332508, A332517.

Sequence in context: A239800 A237501 A300124 * A308371 A052303 A017942

Adjacent sequences: A343514 A343515 A343516 * A343518 A343519 A343520

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2021

Status

approved