A072102 Decimal expansion of sum of reciprocal perfect powers (excluding 1).

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 113.

Links

Table of n, a(n) for n=0..119.

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

Adjacent sequences: A072099 A072100 A072101 * A072103 A072104 A072105

Keyword

nonn,cons

Author

Eric W. Weisstein, Jun 18 2002

Extensions

Corrected by Eric W. Weisstein, May 06 2013

Status

approved