A056607 - OEIS

%I #17 Mar 02 2025 08:00:14

%S 2,3,10,35,231,3003,14586,138567,5311735,154040315,434113615,

%T 16062203755,354604036745,15247973580035,286661903304658,

%U 7596540437573437,79093391614735197,4824696888498847017,85067024086690197405,6039758710155004015755,230948868774022296411965

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

%H Amiram Eldar, <a href="/A056607/b056607.txt">Table of n, a(n) for n = 1..383</a>

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

%e 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.

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

%o (PARI) a(n) = prod(k=1, n, prime(k))/factorback(factor(binomial(n, n\2))[, 1]); \\ _Michel Marcus_, Jul 13 2018

%Y Cf. A002110, A001405, A048633.

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 07 2000