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

1,1

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A002110, A001405, A048633.

Sequence in context: A378730 A134959 A270367 * A278051 A060604 A075890

Adjacent sequences: A056604 A056605 A056606 * A056608 A056609 A056610

Keyword

nonn

Author

Labos Elemer, Aug 07 2000

Status

approved