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In this paper for μ > 0 we study an asymptotic behavior of the sequence defined as Tn(μ) = (τ(n))−1$${\max _{1 \leqslant t \leqslant \left[ {{n^{1/\mu }}} \right]}}$$max1≤t≤[n1/μ] {τ(n +… Click to show full abstract
In this paper for μ > 0 we study an asymptotic behavior of the sequence defined as Tn(μ) = (τ(n))−1$${\max _{1 \leqslant t \leqslant \left[ {{n^{1/\mu }}} \right]}}$$max1≤t≤[n1/μ] {τ(n + t)}, where τ(n) denotes the number of natural divisors of given positive integer n. The motivation of this observation is to explore whether τ-function oscillates rapidly.
Keywords:
function;
property divisor;
divisor function;
asymptotic property
Journal Title: Lobachevskii Journal of Mathematics
Year Published: 2018
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Journal Title: Lobachevskii Journal of Mathematics
Year Published: 2018
Link to full text (if available)
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