On the sum of values of a multidimensional divisor function on a sequence of type \([n^c]\) (Q1584134)

The main result of the paper is the following theorem. For \(1<c<8/7\) the asymptotic formula \[ A(T)=\sum_{n\leq T} \tau_k\left(\left[n^c\right]\right) = TQ_{k-1}(\ln T)+O\bigg(\frac{T}{\ln T}\bigg) \] is valid, where \(\tau_k(n)\) is the number of solutions in natural numbers \(x_1,\dots,x_k\) of the equation \(x_1\dots x_k=n\), \(Q_{k-1}(x)\) is a polynomial of degree \(k-1\), and \([x]\) is the integer part of~\(x\).