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%I #8 Dec 29 2020 16:12:34
%S 2,9,0,5,7,3,6,7,8,9,4,8,8,4,0,3,6,1,7,7,5,4,1,7,7,7,9,7,7,0,5,8,9,0,
%T 6,9,6,6,1,6,9,7,7,2,7,5,0,2,0,7,7,5,5,2,3,1,7,9,7,8,0,9,0,8,4,3,5,2,
%U 7,4,0,8,3,7,6,1,2,1,2,5,7,7,8,1,1,0
%N Decimal expansion of sum of reciprocals of squares of perfect numbers.
%C The sum of reciprocals of A000396(n)^2 converges since the sum of reciprocals of A000396(n) converges (see A335118).
%D Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 244.
%H 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 Equals Sum_{k>=1} 1/A000396(k)^2.
%e 0.0290573678948840361775417779770589069661697...
%t RealDigits[Sum[1/(2^(p - 1)*(2^p - 1))^2, {p, MersennePrimeExponent[Range[14]]}], 10, 100][[1]]
%Y Cf. A000396, A173898, A335118.
%K cons,nonn
%O -1,1
%A _Marco Ripà_, Dec 26 2020
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