A092435 Prime factorials divided by their corresponding primorials.

1, 1, 4, 24, 17280, 207360, 696729600, 12541132800, 115880067072000, 1366643159020339200000, 40999294770610176000000, 1854768736099424576471040000000, 109950690675973888893203251200000000, 4617929008390903333514536550400000000, 420600974084243475616503989010432000000000

Offset: 1

Author

Don Willard (dwillard(AT)prairie.cc.il.us), Mar 23 2004

Keywords

• nonn

Examples

			E.g., 2 factorial divided by 2 primorial is 1; 3 factorial is 6, divided by 3 primorial (3*2=6) is also 1; 5 factorial is 120, divided by 5 primorial (5*3*2=30) is 4 and so forth.
		

Crossrefs

Subsequence of A036691. - Chayim Lowen, Jul 23 2015

Cf. A002110, A039716.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, 1,
      a(n-1)*mul(i, i=ithprime(n-1)+1..ithprime(n)-1))
    end:
seq(a(n), n=1..15);  # Alois P. Heinz, Jan 15 2025

Mathematica

Table[ Prime[n]! / Times @@ Prime[ Range[ n]], {n, 13}] (* Robert G. Wilson v, Mar 25 2004 *)

PARI

a(n)=prime(n)!/prod(i=1,n,prime(i)) \\ Ralf Stephan, Dec 21 2013

Formula

p!/p# = A039716/A002110.

Partial products of A061214. - Lekraj Beedassy, Nov 06 2006

From Chayim Lowen, Jul 23 - Aug 05 2015: (Start)

a(n) = A036691(A065890(n)).

a(n) = A000142(A002808(A065890(n)))/A034386(A002808(A065890(n))).

a(n) = Product_{k=1..n} prime(k)^(A085604(prime(n),k)-1).

a(n) = A049614(prime(n)).

a(n) = Product_{k=1..prime(n)} k^A066247(k). (End)

Extensions

Edited by Robert G. Wilson v, Mar 25 2004

More terms from Michel Marcus, Jan 15 2025