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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 (list; constant; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=-1..84.

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

Cf. A000396, A173898, A335118.

Sequence in context: A140239 A221200 A221245 * A021348 A346833 A192938

Adjacent sequences:  A340006 A340007 A340008 * A340010 A340011 A340012

KEYWORD

cons,nonn

AUTHOR

Marco Ripà, Dec 26 2020

STATUS

approved

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Last modified December 1 13:38 EST 2021. Contains 349429 sequences. (Running on oeis4.)