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

1,1

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

Links

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

Index entries for sequences related to lcm's

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A020500, A025547.

Sequence in context: A338974 A255562 A130140 * A326577 A090368 A120374

Adjacent sequences: A051414 A051415 A051416 * A051418 A051419 A051420

Keyword

easy,nice,nonn

Author

Asher Auel

Extensions

More terms from James A. Sellers

Status

approved