A056060 The powerfree part of the central binomial coefficients.

1, 2, 3, 6, 10, 5, 35, 70, 14, 7, 462, 231, 429, 429, 715, 1430, 24310, 12155, 92378, 46189, 88179, 88179, 1352078, 676039, 52003, 52003, 7429, 7429, 1077205, 1077205, 33393355, 66786710, 43214930, 21607465, 181502706, 90751353, 176726319, 176726319, 7658140490

Offset: 1

Author

Labos Elemer, Jul 26 2000

Keywords

• nonn

Examples

			n=14, binomial(14,7) = 3432 = 8*3*11*13. The largest square divisor is 4, and the squarefree part is 858. So GCD(4,858) = 2 and a(14) = 858/2 = 429.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3388

Crossrefs

Cf. A001405, A000188, A008833, A007913, A055229, A055231, A046098, A034974, A056056, A056057, A056058, A056059, A056060, A056061.

Programs

Mathematica

a[n_] := Denominator[(b = Binomial[n, Floor[n/2]])/(Times @@ First /@ FactorInteger[b])^2]; Array[a, 36] (* Amiram Eldar, Sep 05 2020 *)

Formula

a(n) = A055231(A001405(n)).

Extensions

New name and more terms from Amiram Eldar, Sep 05 2020