### On the irrationality of a divisor function series.

Friedlander, John B., Luca, Florian, Stoiciu, Mihai (2007)

Integers

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Friedlander, John B., Luca, Florian, Stoiciu, Mihai (2007)

Integers

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Acta Mathematica et Informatica Universitatis Ostraviensis

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Romanoff (1934) showed that integers that are the sum of a prime and a power of 2 have positive lower asymptotic density in the positive integers. We adapt his method by showing more generally the existence of a positive lower asymptotic density for integers that are the sum of a prime and a term of a given nonconstant nondegenerate integral linear recurrence with separable characteristic polynomial.

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