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Perfect Numbers

An integer n is called k-perfect if σ(n) = kn (note that a perfect number
is 2-perfect).
(a) Show that 120 = 23? ? ? 3 ? ? ? 5 is 3-perfect.
(b) Show that if n is 3-perfect and gcd(3, n) = 1, then 3n is 4-perfect.

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