1991
DOI: 10.4064/aa-57-3-267-281
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On prime divisors of Mersenne numbers

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Cited by 9 publications
(8 citation statements)
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“…The background to these Theorems is as follows. As we mentioned, for the case of Mersenne numbers, a form of ( 1.10) was proved in [ 1 ] which is valid for H/ log log log N --> oo and this is stronger than our result. In [13], the second author considered the following average of a recurrence sequence u(h\…”
Section: Theoremcontrasting
confidence: 54%
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“…The background to these Theorems is as follows. As we mentioned, for the case of Mersenne numbers, a form of ( 1.10) was proved in [ 1 ] which is valid for H/ log log log N --> oo and this is stronger than our result. In [13], the second author considered the following average of a recurrence sequence u(h\…”
Section: Theoremcontrasting
confidence: 54%
“…For example, the sequence of integers or the values of a polynomial. In [1] and [6], average values are obtained for the sequence of Mersenne numbers M(h) -2 h -\ over an interval. It was shown that, In (1.10) and (1.11), the error terms are effective and uniform in the sense that they depend only upon the degree of L over Q and n. If n = 2 then the error term in (1.10) is excellent.…”
Section: Q\mmentioning
confidence: 99%
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“…Let f (n) = p|2 n −1 1/p and F (n) = d|2 n −1 1/d, so that f (n) is the reciprocal sum of the primes dividing the nth Mersenne number, and F (n) is the corresponding sum over all divisors. In this note we are concerned with the statistical distribution of f (n) and F (n) as n varies, continuing earlier investigations of Erdős [6,7], Pomerance [24], and Erdős-Kiss-Pomerance [8].…”
mentioning
confidence: 84%
“…Erdős's question seems to have lain dormant for 20 years. In 1991, the study of f (n) was resurrected by Erdős, Kiss, and Pomerance [8]. The main thought there is to study the local distribution of f (n).…”
mentioning
confidence: 99%