If F(n) is a number-theoretic function, and therefore multiplicative (?), with

and

, find

.

This was a test question, and I don't know if thats all the info. We have not gone over this much, so a good explanation of how to evaluate this would be great.

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I tried reducing everything to prime factors:

Because F(n) is multiplicative,

, where

.

Also by the same argument,

, where

.

Just looking at it, i.e. ruling out the common factor 7, I got:

.

Is this right? I relied more on intuition than real number theory, so if it is right, how?