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A072102
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Decimal expansion of sum of reciprocal perfect powers (excluding 1).
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8
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8, 7, 4, 4, 6, 4, 3, 6, 8, 4, 0, 4, 9, 4, 4, 8, 6, 6, 6, 9, 4, 3, 5, 1, 3, 2, 0, 5, 9, 7, 3, 7, 3, 1, 6, 5, 9, 3, 5, 3, 3, 8, 4, 3, 1, 9, 2, 4, 2, 1, 4, 5, 7, 7, 6, 2, 5, 7, 8, 8, 2, 5, 3, 5, 0, 9, 3, 7, 0, 0, 6, 4, 1, 2, 9, 7, 2, 3, 6, 7, 6, 5, 9, 9, 3, 3, 2, 2, 6, 1, 7, 8, 5, 7, 5, 8, 0, 1, 6, 2, 8, 7, 7, 0, 6, 3, 4, 1, 9, 3, 6, 2, 5, 5, 9, 0, 5, 3, 0, 1
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 113.
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LINKS
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FORMULA
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Equals Sum_{k>=2} mu(k)*(1-zeta(k)). (End)
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EXAMPLE
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0.874464368404944866694351320597373165935338431924214...
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MATHEMATICA
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RealDigits[Total[Block[{$MaxExtraPrecision = 10^3}, N[#, 120] & /@ Table[MoebiusMu[k] (1 - Zeta[k]), {k, 2, 10^3}]]]][[1]]
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PROG
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(PARI) cons()=my(bp=bitprecision(1.), s=0.); forsquarefree(k=2, bp, s+=moebius(k)*(1-zeta(k[1]))); s \\ Charles R Greathouse IV, Feb 08 2023
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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