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A072044 Numerator of Product{prime(k)^2/(prime(k)^2 - 1) | 0<k<=n}, Denominator: A072045. 3
4, 3, 25, 1225, 29645, 715715, 206841635, 14933966047, 718188003533, 86285158710179, 82920037520482019, 5974606913975783369, 10043314222393291843289, 1688189817927745147112851 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n)/A072045(n) -> (Pi^2)/6 (Leonhard Euler, 1748).

REFERENCES

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

LINKS

Table of n, a(n) for n=1..14.

EXAMPLE

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)=25;

a(10)/A072045(10)=86285158710179/52836150804480=1.63307049.

MATHEMATICA

Numerator/@Rest[FoldList[Times, 1, #/(#-1)&/@(Prime[Range[15]]^2)]] (* Harvey P. Dale, May 03 2011 *)

CROSSREFS

Cf. A000040, A001248, A236435, A236436.

Sequence in context: A286328 A189742 A243237 * A286795 A127138 A064081

Adjacent sequences:  A072041 A072042 A072043 * A072045 A072046 A072047

KEYWORD

nonn,frac

AUTHOR

Reinhard Zumkeller, Jun 09 2002

STATUS

approved

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Last modified November 15 06:32 EST 2019. Contains 329144 sequences. (Running on oeis4.)