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!

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- May 1st 2008, 08:09 AMProof_of_lifeA couple proofs.
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! - May 1st 2008, 09:09 AMThePerfectHacker
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, .

Quote:

(2)

This is Mine 95:):)th Post!!! - May 1st 2008, 09:31 AMPaulRS
We have:

Thus:

And then (2) follows easily