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

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%I A056607 #17 Mar 02 2025 08:00:14
%S A056607 2,3,10,35,231,3003,14586,138567,5311735,154040315,434113615,
%T A056607 16062203755,354604036745,15247973580035,286661903304658,
%U A056607 7596540437573437,79093391614735197,4824696888498847017,85067024086690197405,6039758710155004015755,230948868774022296411965
%N A056607 a(n) is the n-th primorial divided by squarefree kernel of corresponding central binomial coefficient.
%H A056607 Amiram Eldar, <a href="/A056607/b056607.txt">Table of n, a(n) for n = 1..383</a>
%F A056607 a(n) = A002110(n)/A048633(n).
%e A056607 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 A056607 a[n_] := Times @@ Prime[Range[n]] / Times @@ FactorInteger[Binomial[n, Floor[n/2]]][[;;, 1]]; Array[a, 21] (* _Amiram Eldar_, Mar 01 2025 *)
%o A056607 (PARI) a(n) = prod(k=1, n, prime(k))/factorback(factor(binomial(n, n\2))[, 1]); \\ _Michel Marcus_, Jul 13 2018
%Y A056607 Cf. A002110, A001405, A048633.
%K A056607 nonn
%O A056607 1,1
%A A056607 _Labos Elemer_, Aug 07 2000