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A335089
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Decimal expansion of log(Pi^2/6).
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0
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4, 9, 7, 7, 0, 0, 3, 0, 2, 4, 7, 0, 7, 4, 5, 3, 4, 7, 4, 7, 4, 3, 7, 7, 3, 4, 4, 3, 2, 5, 4, 1, 5, 1, 5, 0, 5, 7, 1, 5, 9, 8, 9, 3, 3, 6, 4, 7, 6, 1, 8, 4, 3, 7, 1, 7, 1, 8, 7, 1, 7, 9, 9, 8, 1, 3, 3, 8, 7, 6, 2, 4, 5, 8, 1, 3, 4, 8, 4, 7, 7, 0, 8, 7, 7, 6, 7, 4, 5, 8, 7, 4, 0, 8, 2, 8, 6, 3, 9, 0, 7, 4, 0, 4, 8, 1
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals Sum_{k>=2} MangoldtLambda(k) / ((k^2)*log(k)).
Equals Sum_{k>=1} (1/k)*(1/(A246655(n)^2)) where k is the exponent of the prime power, A025474(n+1).
Equals Sum_{k>=1} primezeta(2*k)/k.
Equals 2*log(Pi) - log(6).
Equals log(zeta(2)) = log(A013661).
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EXAMPLE
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Equals 1/(2^2) + 1/(3^2) + (1/(4^2))*(1/2) + 1/(5^2) + + 1/(7^2) + (1/(8^2))*(1/3) + ... = 0.4977003024707...
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MATHEMATICA
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RealDigits[Log[Pi^2/6], 10, 120][[1]]
RealDigits[Sum[PrimeZetaP[2 k]/k, {k, 1, inf}], 10, 120][[1]]
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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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