In this paper for μ > 0 we study an asymptotic behavior of the sequence defined as T_n(μ) = (τ(n))⁻¹max1≤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.