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

Offset

1,1

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.

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)

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 *)

Prog

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

Crossrefs

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

Sequence in context: A088944 A335000 A352806 * A228847 A093901 A334884

Adjacent sequences: A033928 A033929 A033930 * A033932 A033933 A033934

Keyword

nonn,easy

Author

Jeff Burch

Status

approved