A080397 Largest squarefree number dividing central binomial coefficient A000984(n).

1, 2, 6, 10, 70, 42, 462, 858, 4290, 24310, 92378, 176358, 1352078, 520030, 222870, 6463230, 200360130, 129644790, 907513530, 1767263190, 22974421470, 134564468610, 526024740930, 22870640910, 1074920122770, 1504888171878, 1967930686302, 34766775458002, 1912172650190110

Offset: 0

Author

Labos Elemer, Mar 19 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007947, A000984, A001405, A048633.

Programs

Maple

a := n -> convert(numtheory:-factorset(binomial(2*n, n)), `*`):
seq(a(n),n=0..25); # Peter Luschny, Oct 31 2015

Mathematica

a[n_] := Times @@ FactorInteger[Binomial[2n, n]][[All, 1]]; Array[a, 26, 0] (* Jean-François Alcover, Jun 04 2019 *)

PARI

a(n) = vecprod(factor(binomial(2*n, n))[, 1]); \\ Amiram Eldar, Jun 21 2024

Formula

a(n) = A007947(A000984(n)).

Extensions

More terms from Amiram Eldar, Jun 21 2024