A072045 Denominator of Product{prime(k)^2/(prime(k)^2 - 1) | 0A072044.

1, 3, 2, 16, 768, 18432, 442368, 127401984, 9172942848, 440301256704, 52836150804480, 50722704772300800, 3652034743605657600, 6135418369257504768000, 1030750286035260801024000, 98952027459385036898304000, 21373637931227167970033664000

Offset: 0

Author

Reinhard Zumkeller, Jun 09 2002

Keywords

• nonn
• frac

Comments

A072044(n)/a(n) -> (Pi^2)/6 (Leonhard Euler, 1748).

Examples

			For the first 3 primes: 2,3,5: (2^2/(2^2-1))*(3^2/(3^2-1))*(5^2/(5^2-1)) = (4/3)*(9/8)*(25/24) = (4*9*25)/(3*8*24) = 25/16, therefore a(3)=16;
A072044(9)/a(9)=718188003533/440301256704=1.631128671.
		

References

• M. Sigg: "Pi" p. 191 in Lexikon der Mathematik, Band 4, Spektrum Verlag, 2002.

Crossrefs

Cf. A000040, A001248, A236435, A236436.

Programs

Mathematica

Rest[Denominator[FoldList[Times,1,(#^2/(#^2-1)&/@Prime[Range[20]])]]] (* Harvey P. Dale, Oct 14 2012 *)

Extensions

More terms from Harvey P. Dale, Oct 14 2012

a(0)=1 prepended by Alois P. Heinz, May 11 2024