A056607 a(n) is the n-th primorial divided by squarefree kernel of corresponding central binomial coefficient.

2, 3, 10, 35, 231, 3003, 14586, 138567, 5311735, 154040315, 434113615, 16062203755, 354604036745, 15247973580035, 286661903304658, 7596540437573437, 79093391614735197, 4824696888498847017, 85067024086690197405, 6039758710155004015755, 230948868774022296411965

Offset: 1

Author

Labos Elemer, Aug 07 2000

Keywords

• nonn

Examples

			For n = 6, A002110(6) = 30030, C(6,3) = 20 with squarefree kernel 10. So, a(6) = 30030/10 = 3003 = 3*7*11*13, which is also squarefree.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..383

Crossrefs

Cf. A002110, A001405, A048633.

Programs

Mathematica

a[n_] := Times @@ Prime[Range[n]] / Times @@ FactorInteger[Binomial[n, Floor[n/2]]][[;;, 1]]; Array[a, 21] (* Amiram Eldar, Mar 01 2025 *)

PARI

a(n) = prod(k=1, n, prime(k))/factorback(factor(binomial(n, n\2))[, 1]); \\ Michel Marcus, Jul 13 2018

Formula

a(n) = A002110(n)/A048633(n).