Question 1
Find all integers $n \geq 3$ such that the following property holds:
if we list the divisors of $n!$ in increasing order
as $1 = d_1 \lt d_2 \lt \dots \lt d_k = n!$, then we have
$$d_2 - d_1 \leq d_3 - d_2 \leq … \leq d_k - d_{k-1}.$$
Proposed by Luke Robitaille. One nonofficial editorial point; manual essay grading.
if we list the divisors of $n!$ in increasing order
as $1 = d_1 \lt d_2 \lt \dots \lt d_k = n!$, then we have
$$d_2 - d_1 \leq d_3 - d_2 \leq … \leq d_k - d_{k-1}.$$
Proposed by Luke Robitaille. One nonofficial editorial point; manual essay grading.