Shourya's function

Algebra Level 5

Function ff from the positive integers to the positive integers satisfies the following conditions:

(1) f(xy)=f(x)+f(y)1f(xy)=f(x)+f(y)-1, for any pair of positive integers xx and yy.

(2) f(x)=1f(x)=1 holds for only finitely many xx.

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

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

This problem is posed by Shourya P.

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