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.
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?