Numbers n such that cr(cr(n)) = 2n are called superpeifect numbers.(a) If n = 2k with

Chapter 11, Problem 14

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Numbers n such that cr(cr(n)) = 2n are called superpeifect numbers.(a) If n = 2k with 2k+1 - 1 a prime, prove that n is superperfect; hence, 16 and 64 aresuperperf ect.(b) Find all even perfect numbers n = 2k-1(2k - 1) which are also superperfect.[Hint: First establish the equality cr(cr(n)) = 2k(2k+1 - l).]

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