|
%I #26 Feb 16 2020 20:16:23
%S 1,4,96,18432,31850496,550376570880,114126085737676800,
%T 331312591939905257472000,14427205603578338379772723200000,
%U 10051861189298894268003697526046720000000
%N Partial products of A036691.
%C Product of the first n compositorial numbers (which are themselves the product of the first n composite numbers). This is to compositorial numbers (A036691), as superfactorials (A000178) are to factorials (A000142).
%F a(n) = Product_{i=0..n} A036691(i) = Product_{i=0..n} Product_{j=1..i} A002808(j).
%e a(3) = 1 * 4 * 24 * 192 = (1) * (1*4) * (1*4*6) * (1*4*6*8), since the first 4 composite numbers are (4, 6, 8) and the 0th compositorial is 1.
%t nn=20;cnos=Complement[Range[nn],Prime[Range[PrimePi[nn]]]];Rest[ FoldList[ Times,1,Rest[FoldList[Times,1,cnos]]]] (* _Harvey P. Dale_, Jun 28 2011 *)
%Y Cf. A000142, A000178, A002808, A036691.
%K nonn,easy
%O 0,2
%A _Jonathan Vos Post_, Jan 28 2011
|
