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Math Help - multiple of perfect number is abundant

  1. #1
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    multiple of perfect number is abundant

    A positive integer n is abundant if sigma(n) > 2n (where sigma(n) = sum of divisors of n)
    An integer k is prefect if sigma(k) = 2k
    I need to prove that a multiple of a perfect number is abundant.

    Suppose n is a prefect number and k is a nonnegative integer.
    If gcd(n,k)=1 then sigma(nk) = sigma(n) * sigma(k) = 2n * sigma(k) > 2nk
    Otherwise... this is where I'm having some trouble.. any suggestions?
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  2. #2
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    Re: multiple of perfect number is abundant

    I arrived at the solution. It was much simpler than what I attempted in the original post.
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  3. #3
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    Re: multiple of perfect number is abundant

    well done!
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