A109044 a(n) = lcm(n,3).

0, 3, 6, 3, 12, 15, 6, 21, 24, 9, 30, 33, 12, 39, 42, 15, 48, 51, 18, 57, 60, 21, 66, 69, 24, 75, 78, 27, 84, 87, 30, 93, 96, 33, 102, 105, 36, 111, 114, 39, 120, 123, 42, 129, 132, 45, 138, 141, 48, 147, 150, 51, 156, 159, 54, 165, 168, 57, 174, 177, 60, 183, 186, 63

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Index entries for sequences related to lcm's.

Formula

a(n) = 3*n/gcd(n,3) = 3*n/A109007(n).

From Bruno Berselli, Mar 11 2011: (Start)

G.f.: 3*x*(1+2*x+x^2+2*x^3+x^4)/(1-x^3)^2.

a(n) = 3*A051176(n);

a(n) = n*(7-2*A099837(n))/3 for n>0. (End)

From Wesley Ivan Hurt, Jul 24 2016: (Start)

a(n) = 2*a(n-3) - a(n-6) for n>5.

a(n) = 9*n/(5 + 4*cos(2*n*Pi/3)).

If n mod 3 = 0 then 3*floor(n/3), else 3*n. (End)

a(n) = n*(1 + 2*((n^2) mod 3)). - Timothy Hopper, Feb 23 2017

From Michael Somos, Mar 04 2017: (Start)

G.f.: 3 * x / (1 - x)^2 - 6 * x^3 / (1 - x^3)^2. -

a(n) = a(-n) for all n in Z. (End)

Sum_{k=1..n} a(k) ~ (7/6) * n^2. - Amiram Eldar, Nov 26 2022

Sum_{n>=1} (-1)^(n+1)/a(n) = 5*log(2)/9. - Amiram Eldar, Sep 08 2023

Example

G.f. = 3*x + 6*x^2 + 3*x^3 + 12*x^4 + 15*x^5 + 6*x^6 + 21*x^7 + 24*x^8 + ...

Maple

A109044:=n->lcm(n, 3): seq(A109044(n), n=0..100); # Wesley Ivan Hurt, Jul 24 2016

Mathematica

LCM[Range[0, 100], 3] (* Wesley Ivan Hurt, Jul 24 2016 *)

Prog

(SageMath) [lcm(n, 3)for n in range(0, 64)] # Zerinvary Lajos, Jun 07 2009
(Magma) [Lcm(n, 3): n in [0..63]]; // Bruno Berselli, Mar 11 2011
(PARI) a(n)=lcm(n, 3) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A051176, A099837, A109007 (gcd(n,3)), A109042.

Sequence in context: A203491 A085709 A120910 * A205844 A205865 A376547

Adjacent sequences: A109041 A109042 A109043 * A109045 A109046 A109047

Keyword

nonn,easy

Author

Mitch Harris, Jun 18 2005

Status

approved