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Flawless Series? (Posted on 2003-11-29) Difficulty: 3 of 5
What are the next three numbers in this sequence? 6, 28, 496, 8128, ... ? Please explain how you determined these three numbers.

See The Solution Submitted by SilverKnight    
Rating: 2.8889 (9 votes)

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Question Explain... | Comment 16 of 67 |
Not to be rude (like some people are), but neither of your explanations were very easy to understand for me.

Is (2^(p-1))*(2^p-1) the definition of perfect numbers, or does it just succeed in finding many perfect numbers? It seems like an unnecessarily complex equation if it's defining it rather than finding it. Also, if it was defining it, than it would be simple to prove that there are no odd perfect numbers.

But then, even if there were more perfect numbers besides the ones that are found by that equation, it isn't necessarily relevant to the sequence. The sequence could be the following: all perfect numbers, perfect numbers found by the equation, or the outputs of the equation when p is prime. BTW, no one said directly that p had to be prime, which further confused me.

If I'm missing something obvious, maybe that something wasn't as obvious as you thought.
  Posted by Tristan on 2003-11-30 12:34:54
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