Maximizing a Strange Function
Number Theory
Level
5
Define a function \(f(n)\) for some positive, integral \(n\) as the number of positive integral \(a<n\) for which the expression
\[\dfrac{n-a}{a}\]
is also a positive integer. What is the maximum value of \(f(n)\) for \(n \leq 1000\)?
by
Finn Hulse