login
Product of the first n (semiprimes - 1).
1

%I #11 Jan 21 2023 13:17:44

%S 3,15,120,1080,14040,196560,3931200,82555200,1981324800,49533120000,

%T 1585059840000,52306974720000,1778437140480000,65802174197760000,

%U 2500482619514880000,112521717878169600000,5401042458152140800000

%N Product of the first n (semiprimes - 1).

%C Semiprime analog of A005867.

%F a(n) = Prod[from i = 1 to n] (A001358(i)-1).

%e a(10) = 3*5*8*9*13*14*20*21*24*25 =

%e (4-1)*(6-1)*(9-1)*(10-1)*(14-1)*(15-1)*(21-1)*(22-1)*(25-1)*(26-1) = 49533120000, the product of the first 10 (semiprimes minus one).

%t FoldList[Times,Select[Range[50],PrimeOmega[#]==2&]-1] (* _Harvey P. Dale_, Jan 21 2023 *)

%o (PARI) A001358(n)={

%o if(n==1,

%o return(4),

%o for(a=A001358(n-1)+1,100000000000000000,

%o if (bigomega(a)==2,

%o return(a)

%o ) ;

%o ) ;

%o ) ;

%o }

%o A112228(n)={

%o prod(i=1,n,A001358(i)-1)

%o } /* R. J. Mathar, Mar 09 2012 */

%Y Cf. A001358, A005867.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Nov 28 2005