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%I #20 Feb 08 2023 16:20:51
%S 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,
%T 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,
%U 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
%N Decimal expansion of sum of reciprocal perfect powers (excluding 1).
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 113.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>.
%F From _Amiram Eldar_, Aug 20 2020: (Start)
%F Equals Sum_{k>=2} 1/A001597(k).
%F Equals Sum_{k>=2} mu(k)*(1-zeta(k)). (End)
%e 0.874464368404944866694351320597373165935338431924214...
%t RealDigits[Total[Block[{$MaxExtraPrecision = 10^3}, N[#, 120] & /@ Table[MoebiusMu[k] (1 - Zeta[k]), {k, 2, 10^3}]]]][[1]]
%o (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
%Y Cf. A001597.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Jun 18 2002
%E Corrected by _Eric W. Weisstein_, May 06 2013
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