jmc

Given a real number $x$, let $\lfloor x\rfloor$ denote the greatest integer less than or equal to $x$. For a certain integer $k$, there are exactly 70 positive integers $n_1$, $n_2,\dots ,$ $n_{70}$ such that $$k=\lfloor \sqrt[3]{n_1}\rfloor =\lfloor \sqrt[3]{n_2}\rfloor =\cdots =\lfloor \sqrt[3]{n_{70}}\rfloor$$and $k$ divides $n_i$ for all $i$ such that $1\le i\le 70$.

Find the maximum value of $\frac{n_i}{k}$ for $1\le i\le 70$.