login
Let C(n) = product of composite numbers between the n-th prime and (n+1)-th prime; a(n) = floor(C(n+1)/C(n)).
0

%I #7 Nov 17 2018 21:35:24

%S 1,120,0,280,0,513,1276,0,1507968,0,0,2168,3424,1,0,17873856,0,0,

%T 35185150,0,8847,12778,0,0,11348,0,12662,777455654403407438918,0,

%U 20121,0,192643714695223095,0,577325548,1,0,31603,1,0,1478997122921398080,0

%N Let C(n) = product of composite numbers between the n-th prime and (n+1)-th prime; a(n) = floor(C(n+1)/C(n)).

%e a(4) = floor(14*15*16/12) = 280.

%t c[n_] := Times @@ Select[Range[Prime[n], Prime[n + 1]], PrimeQ[ # ]==False&]; Table[Floor[c[n + 1]/c[n]], {n, 2, 30}] (* _Ryan Propper_, Jul 21 2006 *)

%o (PARI) C=4;for(n=3,100,Cp1=1;for(k=prime(n)+1,prime(n+1)-1,Cp1*=k);print1(floor(Cp1/C)",");C=Cp1) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 02 2007

%K nonn

%O 1,2

%A _Amarnath Murthy_, Aug 12 2002

%E More terms from _Ryan Propper_, Jul 21 2006

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 02 2007