ON THE LARGEST PRIME FACTOR OF THE MERSENNE NUMBERS

摘要

Let P.k/ be the largest prime factor of the positive integer k. In this paper, we prove that the seriesnXnnu00151n.log nnP.2n 1is convergent for each constant n < 1=2, which gives a more precise form of a result of C. L. Stewartn[‘On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers’, Proc. London Math. Soc. 35(3) (1977),n425–447].