Question 4
A positive integer $n \gt 1$, whose positive divisors are
$$
1 = d_1 \lt d_2 \lt \dots \lt d_k = n,
$$
is called *sureño* if all of the numbers $d_2 - d_1, d_3 - d_2, \dots, d_k - d_{k-1}$ are divisors of $n$.
a. Find a positive integer that is not sureño and has exactly 2022 positive divisors that are sureño.
b. Prove that there are infinitely many positive integers that are not sureño and have exactly 2022 positive divisors that are sureño.
$$
1 = d_1 \lt d_2 \lt \dots \lt d_k = n,
$$
is called *sureño* if all of the numbers $d_2 - d_1, d_3 - d_2, \dots, d_k - d_{k-1}$ are divisors of $n$.
a. Find a positive integer that is not sureño and has exactly 2022 positive divisors that are sureño.
b. Prove that there are infinitely many positive integers that are not sureño and have exactly 2022 positive divisors that are sureño.