A157625 Product of the composite numbers between n+1 and 2n, both inclusive.

1, 4, 24, 48, 4320, 8640, 120960, 3628800, 7257600, 14515200, 6706022400, 13412044800, 8717829120000, 470762772480000, 941525544960000, 1883051089920000, 2112783322890240000, 147894832602316800000

Offset: 1

Author

Jaume Oliver Lafont, Mar 03 2009

Keywords

• nonn

Comments

This function is very useful in a problem due to Paul Erdős recorded in A157017. - M. F. Hasler, Feb 26 2014

Crossrefs

Cf. A073840, A157017, A144186 (product of primes between n+2 and 2n, both inclusive).

Programs

Mathematica

nn=20;With[{comps=Complement[Range[2nn],Prime[Range[PrimePi[2nn]]]]}, Table[ Times@@ Select[comps,#>n&&#<=2n&],{n,nn}]] (* Harvey P. Dale, Feb 18 2013 *)

PARI

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

Formula

a(n) = n!*A000984(n)*A034386(n)/A034386(2n). - M. F. Hasler, Feb 26 2014