The average of the fc-fold divisor function dk (n) = ≠ (a1, …ak) ∈ ℤ>0k: a1⋯ak = n has been widely studied. The Piatetski-Shapiro sequences are of the form Nc = (⌊ nc ⌋) n=1∞ with c > 1, c ∉ ℕ. In this article, we estimate the average of the k-fold divisor function over the intersection of Piatetski-Shapiro sequences.
Guo et al. (Mon,) studied this question.