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Math Help - Sum of Positive Divisors Function

  1. #1
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    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?)]
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  2. #2
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    Re: Sum of Positive Divisors Function

    Hey younghorsey.

    What is v(d)? Is this some kind of special analytic number theory function?
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  3. #3
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    Re: Sum of Positive Divisors Function

    Hey chiro.

    \upsilon(n) = \sum_{d|n, d>0} 1
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  4. #4
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    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.
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  5. #5
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    Re: Sum of Positive Divisors Function

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

    Sum of Positive Divisors Function-mhfnumbertheory2a.png
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