slightly excessive numbers
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slightly excessive numbers
I have read that although there are slightly defective numbers (divisors add up to one less that the number, counting each divsor only once, e.g. 4: 1+2=3), there do not appear to be any slightly excessive numbers even though their existence has not been proven or disproven. Why don't prime numbers count (such as 7*1=7 and 7+1=8)?
Re: slightly excessive numbers
Because you don't count the number itself. The sum of the divisors of a prime number is 1, purely and simply.
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Re: slightly excessive numbers
Yeah, if you counted the number itself, every number would work.
 kernelpanic
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Re: slightly excessive numbers
Anubis wrote:Yeah, if you counted the number itself, every number would work.
Except 1. And 0.
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Re: slightly excessive numbers
kernelpanic wrote:Anubis wrote:Yeah, if you counted the number itself, every number would work.
Except 1. And 0.
And every other nonprime number.
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Re: slightly excessive numbers
If you count the number itself, there would be no slightly defective numbers. I think that is what they were trying to get at.

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Re: slightly excessive numbers
nash1429 wrote:I have read that although there are slightly defective numbers (divisors add up to one less that the number, counting each divsor only once, e.g. 4: 1+2=3), there do not appear to be any slightly excessive numbers even though their existence has not been proven or disproven. Why don't prime numbers count (such as 7*1=7 and 7+1=8)?
I think you might be confusing just divisors and prime divisors?
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