A073840 - OEIS

%I #9 Dec 05 2013 19:55:31

%S 1,4,24,192,4320,51840,120960,29030400,65318400,145152000,6706022400,

%T 160944537600,8717829120000,6590678814720000,14122883174400000,

%U 30128817438720000,2112783322890240000,2662106986841702400000

%N Product of the composite numbers between n and 2n (both inclusive).

%C a(n) is divisible by central binomial coefficients, A001405[n]

%F a(n)=A049614(2n)/A049614(n-1)

%e a(6) = 6*8*9*10*12 = 51840.

%p for n from 1 to 50 do l := 1:for j from n to 2*n do if not isprime(j) then l := l*j:fi:od:a[n] := l:od:seq(a[j],j=1..50);

%t cs[x_] := Flatten[Position[Table[PrimeQ[j], {j, x, 2*x}], False]]+x-1; prcs[x_] := Apply[Times, cs[x]]; Table[prcs[w], {w, 1, 25}]

%o (PARI) a(n)=prod(i=n,2*n,i^if(isprime(i),0,1))

%Y Cf. A073839, A073641.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Aug 13 2002

%E More terms from _Sascha Kurz_ and _Labos Elemer_, Aug 14 2002