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CAT 2024 Set-2 | Quantitative Aptitude | Question: 2

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A function $f$ maps the set of natural numbers to whole numbers, such that $f(x y)=f(x) f(y)+f(x)+f(y)$ for all $x, y$ and $f(p)=1$ for every prime number $p$. Then, the value of $f(160000)$ is

  1. $8191$
  2. $2047$
  3. $4095$
  4. $1023$

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