On the largest prime factor of the Mersenne numbers

Details On the largest prime factor of the Mersenne numbers On the largest prime factor of the Mersenne numbers

2007-04-10

arxiv.org/abs/0704.1327v1

Bull. Austr. Math. Soc. 79 (2009), 455-463

Mathematics

Number Theory

11 pages

Scientific paper

Let P(k) be the largest prime factor of the positive integer k. In this
paper, we prove that the series $\sum_{n\ge 1}\frac{(\log n)^a}{P(2^n-1)}$ is
convergent for each constant a<1/2, which gives a more precise form of a result
of C. L. Stewart from 1977.

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