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A340009
Decimal expansion of sum of reciprocals of squares of perfect numbers.
0
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, 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, 7, 4, 0, 8, 3, 7, 6, 1, 2, 1, 2, 5, 7, 7, 8, 1, 1, 0
OFFSET
-1,1
COMMENTS
The sum of reciprocals of A000396(n)^2 converges since the sum of reciprocals of A000396(n) converges (see A335118).
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)^2.
EXAMPLE
0.0290573678948840361775417779770589069661697...
MATHEMATICA
RealDigits[Sum[1/(2^(p - 1)*(2^p - 1))^2, {p, MersennePrimeExponent[Range[14]]}], 10, 100][[1]]
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Marco Ripà, Dec 26 2020
STATUS
approved