The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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