On the values of the divisor function |
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Authors: | Florian Luca Igor E Shparlinski |
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Institution: | (1) Universidad Nacional Autónoma de México, Morelia, México;(2) Macquarie University, Sydney, Australia |
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Abstract: | For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we obtain lower and upper bounds for the average value of the
ratio τ(n + 1)/τ(n) as n ranges through positive integers in the interval 1,x]. We also study the cardinality of the sets {τ(p − 1) : p ≤ x prime} and {τ(2n − 1) : n ≤ x}.
Authors’ addresses: Florian Luca, Instituto de Matemáticas, Universidad Nacional Autónoma'de'México, C.P. 58089, Morelia,
Michoacán, México; Igor E. Shparlinski, Department of Computing, Macquarie University, Sydney, NSW 2109, Australia |
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Keywords: | 2000 Mathematics Subject Classification: 11N25 11N60 |
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