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 A335118 Decimal expansion of the sum of the reciprocals of the perfect numbers. 2
 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, 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, 2, 7, 4, 4, 0, 4, 5, 1, 3, 1, 9, 8, 5, 4, 0, 7, 0, 7, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. REFERENCES Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 244. LINKS Jonathan Bayless and Dominic Klyve, Reciprocal sums as a knowledge metric: theory, computation, and perfect numbers, The American Mathematical Monthly, Vol. 120, No. 9 (2013), pp. 822-831, alternative link, preprint. FORMULA Equals Sum_{k>=1} 1/A000396(k). EXAMPLE 0.20452014283892643017813442909845557667731148935076... MATHEMATICA RealDigits[Sum[1/2^(p - 1)/(2^p - 1), {p, MersennePrimeExponent[Range[14]]}], 10, 100][[1]] CROSSREFS Cf. A000396, A173898. Sequence in context: A164616 A258100 A173335 * A201837 A326052 A004482 Adjacent sequences:  A335115 A335116 A335117 * A335119 A335120 A335121 KEYWORD nonn,cons AUTHOR Amiram Eldar, May 24 2020 STATUS approved

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Last modified May 10 23:31 EDT 2021. Contains 343784 sequences. (Running on oeis4.)