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URL: https://oeis.org/A092435

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A092435
Prime factorials divided by their corresponding primorials.
7
1, 1, 4, 24, 17280, 207360, 696729600, 12541132800, 115880067072000, 1366643159020339200000, 40999294770610176000000, 1854768736099424576471040000000, 109950690675973888893203251200000000, 4617929008390903333514536550400000000, 420600974084243475616503989010432000000000
OFFSET
1,3
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) = 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.
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 *)
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
Sequence in context: A279110 A077093 A077092 * A058230 A162187 A103644
KEYWORD
nonn
AUTHOR
Don Willard (dwillard(AT)prairie.cc.il.us), Mar 23 2004
EXTENSIONS
Edited by Robert G. Wilson v, Mar 25 2004
More terms from Michel Marcus, Jan 15 2025
STATUS
approved