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I have the harmonic mean H(n) of the divisors of a positive integer n. I need to show that if n is perfect number, then H(n) must be an integer.

1/H(n)={1/τ(n)}Σ(1/d)

I have found that

H(n)=nτ(n)/σ(n)

H(n)=τ(n)/2

How can I conclude that this is an integer?

Thank you

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# Harmonic function

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