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Search: id:A127900
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| A127900 |
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Numerators in convergents to 6/Pi^2 using 1/Zeta(s) = Sum_(1,inf.):{mu(n)/n^s}. |
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2
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OFFSET
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1,2
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COMMENT
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The denominator terms are mu(n)/n^2. Denominators of convergents = A127901. n*mu(n) = A055615.
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REFERENCES
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John Derbyshire, "Prime Obsession", Joseph Henry Press, 2003, p. 249.
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FORMULA
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Partial sums of 1/Zeta(s) = Sum_(1,inf.):{mu(n)/n^s}; with s = 2; 1/Zeta(2) = 6/Pi^2.
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EXAMPLE
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1/Zeta(2) = 6/Pi^2 = 1 - 1/2^2 - 1/3^2 - 1/5^2 + 1/6^2 - 1/7^2 + 1/10^2,...
with convergents: 1/1, 3/4, 23/36, 539/900, 47/75, 2228/3675, 9059/14700,...
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CROSSREFS
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Cf. A055615, A127901.
Sequence in context: A116986 A134050 A101191 this_sequence A119669 A013391 A013389
Adjacent sequences: A127897 A127898 A127899 this_sequence A127901 A127902 A127903
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KEYWORD
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nonn,frac
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 04 2007
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