A051417 Quotients of consecutive values of lcm {1, 3, 5 ..., 2n-1} or A025547(n+1)/A025547(n).

3, 5, 7, 3, 11, 13, 1, 17, 19, 1, 23, 5, 3, 29, 31, 1, 1, 37, 1, 41, 43, 1, 47, 7, 1, 53, 1, 1, 59, 61, 1, 1, 67, 1, 71, 73, 1, 1, 79, 3, 83, 1, 1, 89, 1, 1, 1, 97, 1, 101, 103, 1, 107, 109, 1, 113, 1, 1, 1, 11, 1, 5, 127, 1, 131, 1, 1, 137, 139, 1, 1, 1, 1, 149, 151, 1, 1, 157, 1, 1

Offset: 1

Author

Asher Auel

Keywords

• easy
• nice
• nonn

Comments

a(n) = GCD( C(2n+1,1),C(2n+2,2),...,C(3n,n) ) where C(n,k)=binomial(n,k). - Benoit Cloitre, Jan 31 2003

a(n) = greatest common divisor of entries of zigzag matrix Z(n), as defined in A088961. - Reinhard Zumkeller, Oct 25 2013

Examples

			a(5) = A025547(6)/A025547(5) = 3465/315 = 11.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to lcm's

Crossrefs

Cf. A020500, A025547, A014963.

Programs

Haskell

a051417 n = a051417_list !! (n-1)
a051417_list = zipWith div (tail a025547_list) a025547_list
-- Reinhard Zumkeller, Oct 25 2013

Mathematica

Table[Cyclotomic[2n+1,1],{n,90}]  (* Harvey P. Dale, Apr 02 2011 *)
#[[2]]/#[[1]]&/@Partition[Table[LCM@@Range[1,2n+1,2],{n,0,80}],2,1] (* Harvey P. Dale, Mar 04 2013 *)

Formula

a(n) = cyclotomic(2*n+1, 1). - Vladeta Jovovic, Apr 05 2004

a(n) = A014963(2*n+1). - Ridouane Oudra, Jul 02 2025

Extensions

More terms from James Sellers