A061495 a(n) = lcm(3n+1, 3n+2, 3n+3).

6, 60, 504, 660, 2730, 2448, 7980, 6072, 17550, 12180, 32736, 21420, 54834, 34440, 85140, 51888, 124950, 74412, 175560, 102660, 238266, 137280, 314364, 178920, 405150, 228228, 511920, 285852, 635970, 352440, 778596, 428640, 941094, 515100, 1124760, 612468, 1330890

Offset

0,1

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Formula

If n is even, then all three factors are mutually coprime, so lcm = (3n+1)(3n+2)(3n+3), else one half that expression. - Christopher Carl Heckman, Sep 29 2004

G.f.: 6*(10*x^6+28*x^5+125*x^4+70*x^3+80*x^2+10*x+1) / ((x-1)^4*(x+1)^4). - Colin Barker, Feb 25 2013

From Amiram Eldar, Dec 27 2024: (Start)

Sum_{n>=0} 1/a(n) = 11*sqrt(3)*Pi/72 - log(2)/3 - 3*log(3)/8.

Sum_{n>=0} (-1)^n/a(n) = log(2) + (log(3) - sqrt(3)*Pi)/8. (End)

E.g.f.: 3*((4 + 38*x + 90*x^2 + 9*x^3)*cosh(x) + (2 + 76*x + 45*x^2 + 18*x^3)*sinh(x))/2. - Stefano Spezia, Dec 27 2024

Example

a(0) = lcm(1,2,3) = 6; a(1) = lcm(4,5,6) = 60; etc.

Mathematica

Table[LCM@@(3n+{1, 2, 3}), {n, 0, 40}] (* Harvey P. Dale, Dec 23 2022 *)

Prog

(PARI) A061495(n)=lcm(3*n+1, lcm(3*n+2, 3*n+3))

Crossrefs

Sequence in context: A269760 A043033 A179711 * A220411 A248217 A102232

Adjacent sequences: A061492 A061493 A061494 * A061496 A061497 A061498

Keyword

easy,nonn

Author

Jason Earls, Jun 12 2001

Extensions

More terms from several contributors.

Status

approved