Prove that:
(1)
(2)
These come from my Arithmetic functions section in my book. is a divisor function and is multiplicative.
Thanks for any help!
Let and .
The functions are weakly multiplicative meaning whenever .
This means it remains to prove for all primes and positive integers .
.
This if of course true using the identity, .
If is not a square then among its factors for any we can find a mate so that . Thus, we get . If is a square we need to modify the proof a little bit.(2)
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