A073840 Product of the composite numbers between n and 2n (both inclusive).

1, 4, 24, 192, 4320, 51840, 120960, 29030400, 65318400, 145152000, 6706022400, 160944537600, 8717829120000, 6590678814720000, 14122883174400000, 30128817438720000, 2112783322890240000, 2662106986841702400000

Offset: 1

Author

Amarnath Murthy, Aug 13 2002

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A073839, A073641.

Programs

Maple

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);

Mathematica

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}]

PARI

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

Formula

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

Extensions

More terms from Sascha Kurz and Labos Elemer, Aug 14 2002