cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A072102 #21 Feb 16 2025 08:32:46
%S A072102 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 A072102 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 A072102 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 A072102 Decimal expansion of sum of reciprocal perfect powers (excluding 1).
%D A072102 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 113.
%H A072102 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>.
%F A072102 From _Amiram Eldar_, Aug 20 2020: (Start)
%F A072102 Equals Sum_{k>=2} 1/A001597(k).
%F A072102 Equals Sum_{k>=2} mu(k)*(1-zeta(k)). (End)
%e A072102 0.874464368404944866694351320597373165935338431924214...
%t A072102 RealDigits[Total[Block[{$MaxExtraPrecision = 10^3}, N[#, 120] & /@ Table[MoebiusMu[k] (1 - Zeta[k]), {k, 2, 10^3}]]]][[1]]
%o A072102 (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 A072102 Cf. A001597.
%K A072102 nonn,cons
%O A072102 0,1
%A A072102 _Eric W. Weisstein_, Jun 18 2002
%E A072102 Corrected by _Eric W. Weisstein_, May 06 2013