Given a square-free integer $n>2$, evaluate the sum $\sum_{k=1}^{(n-2)(n-1)} \lfloor ({kn})^{1/3} \rfloor$.
Problem
Source: Romanian 2018 TST Problem 2 Day 3
Tags: number theory, floor function, series summation
Source: Romanian 2018 TST Problem 2 Day 3
Tags: number theory, floor function, series summation
Given a square-free integer $n>2$, evaluate the sum $\sum_{k=1}^{(n-2)(n-1)} \lfloor ({kn})^{1/3} \rfloor$.