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

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Abstract
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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