A109050 a(n) = lcm(n,9).

0, 9, 18, 9, 36, 45, 18, 63, 72, 9, 90, 99, 36, 117, 126, 45, 144, 153, 18, 171, 180, 63, 198, 207, 72, 225, 234, 27, 252, 261, 90, 279, 288, 99, 306, 315, 36, 333, 342, 117, 360, 369, 126, 387, 396, 45, 414, 423, 144, 441, 450, 153, 468, 477, 54, 495, 504

Offset

0,2

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Index entries for sequences related to lcm's.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-1).

Formula

a(n) = n*9/gcd(n,9).

a(n) = 9*n/A109012(n) = 9*A106610(n). - R. J. Mathar, Apr 18 2011

Sum_{k=1..n} a(k) ~ (61/18) * n^2. - Amiram Eldar, Nov 26 2022

Sum_{n>=1} (-1)^(n+1)/a(n) = 7*log(2)/27. - Amiram Eldar, Sep 08 2023

From Elmo R. Oliveira, Jun 02 2026: (Start)

a(n) = 2*a(n-9) - a(n-18).

G.f.: 9*x * (1 - x + x^2) * (1 + 3*x + 3*x^2 + 4*x^3 + 6*x^4 + 4*x^5 + 5*x^6 + 9*x^7 + 5*x^8 + 4*x^9 + 6*x^10 + 4*x^11 + 3*x^12 + 3*x^13 + x^14) / (1 - x^9)^2. (End)

Mathematica

LCM[9, Range[0, 60]] (* Harvey P. Dale, Aug 21 2021 *)

Prog

(SageMath) [lcm(n, 9)for n in range(0, 57)] # Zerinvary Lajos, Jun 09 2009
(Magma) [Lcm(n, 9): n in [0..100]]; // Vincenzo Librandi, Apr 18 2011

Crossrefs

Cf. A106610, A109012, A109042.

Sequence in context: A023418 A302232 A069528 * A103700 A158623 A046125

Adjacent sequences: A109047 A109048 A109049 * A109051 A109052 A109053

Keyword

nonn,easy

Author

Mitch Harris, Jun 18 2005

Status

approved