# Shourya's function

Algebra 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 $$x$$.

(3) $$f(30)=4$$.

What is the value of $$f(14400)$$?

This problem is posed by Shourya P.

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