Let $N$ be a positive integer. A non-decreasing sequence $a_1 \le a_2 \le \dots$ of positive integers is said to be $N$-rioplatense if there exists an index $i$ such that $N = \frac{i}{a_i}$. Show that every sequence $2024$-rioplatense is $k$-rioplatense for $k=1, 2, 3, \dots, 2023$.