A033931 a(n) = lcm(n,n+1,n+2).

6, 12, 60, 60, 210, 168, 504, 360, 990, 660, 1716, 1092, 2730, 1680, 4080, 2448, 5814, 3420, 7980, 4620, 10626, 6072, 13800, 7800, 17550, 9828, 21924, 12180, 26970, 14880, 32736, 17952, 39270, 21420, 46620, 25308, 54834, 29640, 63960, 34440, 74046, 39732, 85140

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• easy

Comments

Also denominator of h(n+2) - h(n-1), where h(n) is the n-th harmonic number Sum_{k=1..n} 1/k, the numerator is A188386. - Reinhard Zumkeller, Jul 04 2012

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).
• Index entries for sequences related to lcm's.

Crossrefs

Cf. A001008, A002805, A067046, A078637, A007947, A188386, A244009.

Programs

Haskell

a033931 n = lcm n (lcm (n + 1) (n + 2))  -- Reinhard Zumkeller, Jul 04 2012

Magma

[Numerator((n^3-n)/(n^2+1)): n in [2..50]]; // Vincenzo Librandi, Aug 19 2014

Maple

a:= n-> ilcm($n..n+2):
seq(a(n), n=1..50);  # Alois P. Heinz, Jul 18 2025

Mathematica

LCM@@@Partition[Range[50],3,1] (* or *) LinearRecurrence[{0,4,0,-6,0,4,0,-1},{6,12,60,60,210,168,504,360},50] (* Harvey P. Dale, Jun 29 2019 *)

PARI

a(n) = lcm(n^2+n,n+2) \\ Charles R Greathouse IV, Sep 30 2016

Formula

a(n) = n*(n+1)*(n+2)*[3-(-1)^n]/4.

From Reinhard Zumkeller, Jul 04 2012: (Start)

a(n) = 6 * A067046(n).

A007947(a(n)) = A078637(n). (End)

From Amiram Eldar, Sep 29 2022: (Start)

Sum_{n>=1} 1/a(n) = 1 - log(2) (A244009).

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