On the Sum of the Reciprocals of the Fermat Numbers and Related Irrationalities

@article{Golomb1963OnTS,
  title={On the Sum of the Reciprocals of the Fermat Numbers and Related Irrationalities},
  author={Solomon W. Golomb},
  journal={Canadian Journal of Mathematics},
  year={1963},
  volume={15},
  pages={475 - 478},
  url={https://api.semanticscholar.org/CorpusID:123138118}
}
In (1), P. Erdös showed that the function takes on irrational values whenever z = 1/t, t = 2 , 3 , 4 , 5 , . . . . The method of proof uses Lambert's identity, where d(n) is the number of divisors of n; and it is shown that 
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One Reference

On Arithmetical Properties of Lambert Series

rr=l u=l Chowla* has proved that if t is an integer 2 5, then g(x it) is irrational. He also conjectures that for rational 1 x I< J bothJ(x) and g(x) are irrational. In the present note we prove the…