RU-SPB 2012 Problem 105

$S$ is natural, and $S=d_{1}>d_2>...>d_{1000000}=1$ are all divisors of $S$ . What minimal number of divisors can have $d_{250}$ ?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.