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Number Theory

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Euler Phi Function and Number of Prime Divisor Function

NUMTH-RDJGWH

Let $\phi(n)$ be the Euler Phi function of $n$, and $\omega(n)$ be the number of distinct prime factors of $n$.

Find the value of

$$ \sum_{d|27000} \phi(d) \omega(d) $$

A

$7201$

B

$27000$

C

$53100$

D

$76409$

E

$229227$