slightly excessive numbers

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nash1429
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slightly excessive numbers

Postby nash1429 » Mon Mar 01, 2010 2:34 am UTC

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)?

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snowyowl
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Re: slightly excessive numbers

Postby snowyowl » Mon Mar 01, 2010 2:41 am UTC

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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Anubis
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Re: slightly excessive numbers

Postby Anubis » Mon Mar 01, 2010 3:05 am UTC

Yeah, if you counted the number itself, every number would work.

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kernelpanic
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Re: slightly excessive numbers

Postby kernelpanic » Mon Mar 01, 2010 3:28 am UTC

Anubis wrote:Yeah, if you counted the number itself, every number would work.

Except 1. And 0.
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Token
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Re: slightly excessive numbers

Postby Token » Mon Mar 01, 2010 5:12 pm UTC

kernelpanic wrote:
Anubis wrote:Yeah, if you counted the number itself, every number would work.

Except 1. And 0.

And every other non-prime number.
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mdyrud
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Re: slightly excessive numbers

Postby mdyrud » Mon Mar 01, 2010 8:23 pm UTC

If you count the number itself, there would be no slightly defective numbers. I think that is what they were trying to get at.

Suffusion of Yellow
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Re: slightly excessive numbers

Postby Suffusion of Yellow » Wed Mar 03, 2010 1:20 am UTC

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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