A335118 Decimal expansion of the sum of the reciprocals of the perfect numbers.

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

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

Table of n, a(n) for n=0..86.

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]]
RealDigits[Total[1/PerfectNumber[Range[15]]], 10, 120][[1]] (* Harvey P. Dale, Nov 25 2023 *)

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