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Search: id:A072045
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| A072045 |
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Denominator of Product{prime(k)^2/(prime(k)^2 - 1) | 0<k<=n}, Numerator: A072044. |
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+0
2
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| 3, 2, 16, 768, 18432, 442368, 127401984, 9172942848, 440301256704, 52836150804480, 50722704772300800, 3652034743605657600, 6135418369257504768000, 1030750286035260801024000
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OFFSET
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1,1
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COMMENT
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A072044(n)/a(n) -> (pi^2)/6 (Leonhard Euler, 1748).
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REFERENCES
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M. Sigg: "Pi" p. 191 in Lexikon der Mathematik, Band 4, Spektrum Verlag, 2002.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A000040, A001248.
Sequence in context: A126323 A084886 A055864 this_sequence A126354 A158939 A026345
Adjacent sequences: A072042 A072043 A072044 this_sequence A072046 A072047 A072048
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KEYWORD
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nonn,frac
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 09 2002
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