Shourya's functionAlgebra Level 5
Function \(f\) from the positive integers to the positive integers satisfies the following conditions:
(1) \(f(xy)=f(x)+f(y)-1\), for any pair of positive integers \(x\) and \(y\).
(2) \(f(x)=1\) holds for only finitely many \(x\).
What is the value of \(f(14400)\)?
This problem is posed by Shourya P.