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A072102 Decimal expansion of sum of reciprocal perfect powers (excluding 1). 8
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 113.
LINKS
Eric Weisstein's World of Mathematics, Perfect Power.
FORMULA
From Amiram Eldar, Aug 20 2020: (Start)
Equals Sum_{k>=2} 1/A001597(k).
Equals Sum_{k>=2} mu(k)*(1-zeta(k)). (End)
EXAMPLE
0.874464368404944866694351320597373165935338431924214...
MATHEMATICA
RealDigits[Total[Block[{$MaxExtraPrecision = 10^3}, N[#, 120] & /@ Table[MoebiusMu[k] (1 - Zeta[k]), {k, 2, 10^3}]]]][[1]]
PROG
(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
CROSSREFS
Cf. A001597.
Sequence in context: A260060 A260800 A196914 * A274442 A249136 A154815
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jun 18 2002
EXTENSIONS
Corrected by Eric W. Weisstein, May 06 2013
STATUS
approved

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Last modified March 19 07:49 EDT 2024. Contains 370958 sequences. (Running on oeis4.)