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A072044
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Numerator of Product{prime(k)^2/(prime(k)^2 - 1) | 0<k<=n}, Denominator: A072045.
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1
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4, 3, 25, 1225, 29645, 715715, 206841635, 14933966047, 718188003533, 86285158710179, 82920037520482019, 5974606913975783369, 10043314222393291843289, 1688189817927745147112851
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n)/A072045(n) -> (pi^2)/6 (Leonhard Euler, 1748).
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REFERENCES
| M. Sigg: "Pi" p. 191 in Lexikon der Mathematik, Band 4, Spektrum Verlag, 2002.
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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.
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MATHEMATICA
| Numerator/@Rest[FoldList[Times, 1, #/(#-1)&/@(Prime[Range[15]]^2)]] (* From Harvey P. Dale, May 03 2011 *)
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CROSSREFS
| Cf. A000040, A001248.
Sequence in context: A052039 A035048 A189742 * A127138 A064081 A099438
Adjacent sequences: A072041 A072042 A072043 * A072045 A072046 A072047
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KEYWORD
| nonn,frac
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 09 2002
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