Question 1
A list of $n$ positive integers $a_1, a_2, a_3, \dots, a_n$ is called *good* if both of the following conditions are satisfied:
* $a_1 \lt a_2 \lt a_3 \lt \dots \lt a_n$,
* $a_1 + a_2^2 + a_3^3 + \dots + a_n^n \le 2023$.
For each $n \ge 1$, find how many good lists of $n$ numbers are there.
* $a_1 \lt a_2 \lt a_3 \lt \dots \lt a_n$,
* $a_1 + a_2^2 + a_3^3 + \dots + a_n^n \le 2023$.
For each $n \ge 1$, find how many good lists of $n$ numbers are there.