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A013675
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Decimal expansion of zeta(17).
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14
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1, 0, 0, 0, 0, 0, 7, 6, 3, 7, 1, 9, 7, 6, 3, 7, 8, 9, 9, 7, 6, 2, 2, 7, 3, 6, 0, 0, 2, 9, 3, 5, 6, 3, 0, 2, 9, 2, 1, 3, 0, 8, 8, 2, 4, 9, 0, 9, 0, 2, 6, 2, 6, 7, 9, 0, 9, 5, 3, 7, 9, 8, 4, 3, 9, 7, 2, 9, 3, 5, 6, 4, 3, 2, 9, 0, 2, 8, 2, 4, 5, 9, 3, 4, 2, 0, 8, 1, 7, 3, 8, 6, 3, 6, 9, 1, 6, 6, 7
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OFFSET
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1,7
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LINKS
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FORMULA
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Definition: zeta(17) = sum {n >= 1} 1/n^17.
zeta(17) = 2^17/(2^17 - 1)*( sum {n even} n^11*p(n)*p(1/n)/(n^2 - 1)^18 ), where p(n) = n^8 + 36*n^6 + 126*n^4 + 84*n^2 + 9. Cf. A013663, A013667 and A013671.
(End)
zeta(17) = Sum_{n >= 1} (A010052(n)/n^(17/2)) = Sum_{n >= 1} ( (floor(sqrt(n)) - floor(sqrt(n-1)))/n^(17/2) ). - Mikael Aaltonen, Feb 23 2015
zeta(17) = Product_{k>=1} 1/(1 - 1/prime(k)^17). - Vaclav Kotesovec, May 02 2020
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EXAMPLE
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1.0000076371976378997622736002935630292130882490902626790953798439729356...
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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