# Thread: Sum of Positive Divisors Function

1. ## Sum of Positive Divisors Function

Let $n \in Z$ with $n > 0$

Prove that:

$(\sum_{d|n, d>0}\upsilon(d))^2 =$
$\sum_{d|n, d>0}(\upsilon(d))^3$

[Hint: It suffices to prove the equation above for powers of prime numbers (Why?)]

2. ## Re: Sum of Positive Divisors Function

Hey younghorsey.

What is v(d)? Is this some kind of special analytic number theory function?

3. ## Re: Sum of Positive Divisors Function

Hey chiro.

$\upsilon(n) = \sum_{d|n, d>0} 1$

4. ## Re: Sum of Positive Divisors Function

I don't know enough number theory to help you on this one.

What I would recommend you do is collect as many identities as possible and put them all in the one place: this will help you see the connections a lot quicker and should help you solve your problem quicker than say a less structured approach.

If you have all the identities and theorems on a few pages the connections should pop out.

5. ## Re: Sum of Positive Divisors Function

Hi,
The attachment provides a proof. I've left the proofs of several relevant facts to you.