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

Author

Eric W. Weisstein, Jun 18 2002

Keywords

• nonn
• cons

Examples

			0.874464368404944866694351320597373165935338431924214...
		

References

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

Links

• Eric Weisstein's World of Mathematics, Perfect Power.

Crossrefs

Cf. A001597.

Programs

Mathematica

RealDigits[Total[Block[{$MaxExtraPrecision = 10^3}, N[#, 120] & /@ Table[MoebiusMu[k] (1 - Zeta[k]), {k, 2, 10^3}]]]][[1]]

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

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)

Extensions

Corrected by Eric W. Weisstein, May 06 2013