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A092435 Prime factorials divided by their corresponding primorials.

%I A092435 #37 Jan 15 2025 17:47:15
%S A092435 1,1,4,24,17280,207360,696729600,12541132800,115880067072000,
%T A092435 1366643159020339200000,40999294770610176000000,
%U A092435 1854768736099424576471040000000,109950690675973888893203251200000000,4617929008390903333514536550400000000,420600974084243475616503989010432000000000
%N A092435 Prime factorials divided by their corresponding primorials.
%F A092435 p!/p# = A039716/A002110.
%F A092435 Partial products of A061214. - _Lekraj Beedassy_, Nov 06 2006
%F A092435 From _Chayim Lowen_, Jul 23 - Aug 05 2015: (Start)
%F A092435 a(n) = A036691(A065890(n)).
%F A092435 a(n) = A000142(A002808(A065890(n)))/A034386(A002808(A065890(n))).
%F A092435 a(n) = Product_{k=1..n} prime(k)^(A085604(prime(n),k)-1).
%F A092435 a(n) = A049614(prime(n)).
%F A092435 a(n) = Product_{k=1..prime(n)} k^A066247(k). (End)
%e A092435 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.
%p A092435 a:= proc(n) option remember; `if`(n<2, 1,
%p A092435       a(n-1)*mul(i, i=ithprime(n-1)+1..ithprime(n)-1))
%p A092435     end:
%p A092435 seq(a(n), n=1..15);  # _Alois P. Heinz_, Jan 15 2025
%t A092435 Table[ Prime[n]! / Times @@ Prime[ Range[ n]], {n, 13}] (* _Robert G. Wilson v_, Mar 25 2004 *)
%o A092435 (PARI) a(n)=prime(n)!/prod(i=1,n,prime(i)) \\ _Ralf Stephan_, Dec 21 2013
%Y A092435 Subsequence of A036691. - _Chayim Lowen_, Jul 23 2015
%Y A092435 Cf. A002110, A039716.
%K A092435 nonn
%O A092435 1,3
%A A092435 Don Willard (dwillard(AT)prairie.cc.il.us), Mar 23 2004
%E A092435 Edited by _Robert G. Wilson v_, Mar 25 2004
%E A092435 More terms from _Michel Marcus_, Jan 15 2025