A092435 Prime factorials divided by their corresponding primorials.

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

Offset

1,3

Links

Table of n, a(n) for n=1..13.

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)

Example

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.

Mathematica

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

Prog

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

Crossrefs

Subsequence of A036691. - Chayim Lowen, Jul 23 2015

Cf. A002110, A039716.

Sequence in context: A279110 A077093 A077092 * A058230 A162187 A103644

Adjacent sequences: A092432 A092433 A092434 * A092436 A092437 A092438

Keyword

nonn

Author

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

Extensions

Edited by Robert G. Wilson v, Mar 25 2004

Status

approved