For k≥ 2, show each of the following:
(a) n = 2k−1 satisfies the equation σ(n) = 2n− 1.
(b) If 2k − 1 is prime, then n = 2k−1(2k − 1) satisfies the equation σ(n) = 2n.
(c) If 2k − 3 is prime, then n−2k−1(2k−3) satisfies the equation σ(n)=2n + 2.
It is not known if there are any positive integers n for which σ(n) = 2n + 1.
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