A051426 Least common multiple of {2, 4, 6, ..., 2n}.

2, 4, 12, 24, 120, 120, 840, 1680, 5040, 5040, 55440, 55440, 720720, 720720, 720720, 1441440, 24504480, 24504480, 465585120, 465585120, 465585120, 465585120, 10708457760, 10708457760, 53542288800, 53542288800, 160626866400, 160626866400, 4658179125600

Offset: 1

Author

Asher Auel

Keywords

• easy
• nice
• nonn

Comments

Gcd(A025547(n), a(n)) = A025547(floor((n+1)/2)). - Reinhard Zumkeller, Apr 25 2011

Examples

			a(3) = lcm{2,4,6} = 12;
a(7) = lcm{2,4,6,8,10,12,14} = 840.
		

References

• A. Murthy, Some new Smarandache sequences, functions and partitions, Smarandache Notions Journal Vol. 11 N. 1-2-3 Spring 2000 (but beware errors).

Links

• T. D. Noe, Table of n, a(n) for n = 1..500
• Index entries for sequences related to lcm's

Crossrefs

Cf. A003418, A025547.

Programs

Haskell

a051426 n = foldl lcm 1 [2,4..2*n] -- Reinhard Zumkeller, Apr 25 2011

Mathematica

SZ={2};n=2;L=2;Do[L=LCM[L,2n];AppendTo[SZ,L];n++,{99}];SZ (* Zak Seidov, Aug 01 2009 *)
Table[LCM@@Range[2,2n,2],{n,30}] (* Harvey P. Dale, Oct 09 2011 *)

PARI

a(n)=2*lcm([1..n]) \\ Charles R Greathouse IV, Oct 28 2016

Formula

a(n) = a(n-1)*lcm(a(n-1),2n) = a(n-1)* A014963(n). - Zak Seidov, Aug 01 2009

Extensions

a(6), a(7) and a(8) corrected by T. D. Noe, Feb 08 2008

Corrected the example, which did not reflect the sequence values provided. - Michael Davies (mykdavies+oeis(AT)gmail.com), Oct 10 2008

Edited by N. J. A. Sloane, Jul 31 2009 at the suggestion of R. J. Mathar