A051538 Least common multiple of {b(1),...,b(n)}, where b(k) = k(k+1)(2k+1)/6 = A000330(k).

1, 5, 70, 210, 2310, 30030, 60060, 1021020, 19399380, 19399380, 446185740, 2230928700, 6692786100, 194090796900, 12033629407800, 12033629407800, 12033629407800, 445244288088600, 445244288088600, 18255015811632600

Offset: 1

Author

Asher Auel

Keywords

• easy
• nice
• nonn

Comments

Also a(n) = lcm(1,...,(2n+2))/12. - Paul Barry, Jun 09 2006. Proof that this is the same sequence, from Martin Fuller, May 06 2007: k, k+1, 2k+1 are coprime so their lcm is the same as their product. Hence a(n) = lcm{k, k+1, 2k+1 | k=1..n}/6. {k, k+1, 2k+1 | k=1..n} = {1..2n+2 excluding even numbers >n+1}. Adding the higher even numbers to the set doubles the LCM. Hence lcm{k, k+1, 2k+1 | k=1..n}/6 = lcm{1..2n+2}/12.

Examples

			a(4) = lcm(1, 5, 14, 30) = 210.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Second column of A120101.

Cf. A000330.

Cf. A051542 (LCM), A025555.

Programs

Haskell

a051538 n = a051538_list !! (n-1)
a051538_list = scanl1 lcm $ tail a000330_list
-- Reinhard Zumkeller, Mar 12 2014

Magma

[Lcm([1..2*n+2])/12: n in [1..30]]; // G. C. Greubel, May 03 2023

Mathematica

Table[LCM@@Range[2n+2]/12,{n,30}] (* Harvey P. Dale, Apr 25 2011 *)

SageMath

def A051538(n):
    return lcm(range(1,2*n+3))/12
[A051538(n) for n in range(1,31)] # G. C. Greubel, May 03 2023

Extensions

Corrected by James Sellers

Edited by N. J. A. Sloane, May 06 2007