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.
%I A335118 #10 Nov 25 2023 17:55:09
%S A335118 2,0,4,5,2,0,1,4,2,8,3,8,9,2,6,4,3,0,1,7,8,1,3,4,4,2,9,0,9,8,4,5,5,5,
%T A335118 7,6,6,7,7,3,1,1,4,8,9,3,5,0,7,6,3,3,9,7,0,0,6,4,2,4,8,2,4,8,9,8,6,2,
%U A335118 2,7,4,4,0,4,5,1,3,1,9,8,5,4,0,7,0,7,6
%N A335118 Decimal expansion of the sum of the reciprocals of the perfect numbers.
%C A335118 Bayless and Klyve (2013) calculated the first 149 terms of this sequence. The terms beyond this are uncertain due to the possible existence of odd perfect numbers larger than 10^300.
%D A335118 Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 244.
%H A335118 Jonathan Bayless and Dominic Klyve, <a href="https://doi.org/10.4169/amer.math.monthly.120.09.822">Reciprocal sums as a knowledge metric: theory, computation, and perfect numbers</a>, The American Mathematical Monthly, Vol. 120, No. 9 (2013), pp. 822-831, <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.120.09.822">alternative link</a>, <a href="https://www.researchgate.net/publication/259841254_Reciprocal_Sums_as_a_Knowledge_Metric_Theory_Computation_and_Perfect_Numbers">preprint</a>.
%F A335118 Equals Sum_{k>=1} 1/A000396(k).
%e A335118 0.20452014283892643017813442909845557667731148935076...
%t A335118 RealDigits[Sum[1/2^(p - 1)/(2^p - 1), {p, MersennePrimeExponent[Range[14]]}], 10, 100][[1]]
%t A335118 RealDigits[Total[1/PerfectNumber[Range[15]]],10,120][[1]] (* _Harvey P. Dale_, Nov 25 2023 *)
%Y A335118 Cf. A000396, A173898.
%K A335118 nonn,cons
%O A335118 0,1
%A A335118 _Amiram Eldar_, May 24 2020