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Old 2020-06-18, 11:56   #1
drmurat
 
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Default abouth perfect numbers 1

is it known property of perfect number or new ?

a is prime number which is diffferent from 3 .
the number b = 3 x a²
the plus signed integers of sum of divisors of b which is except from b is equal to ( a + 2 )²


just like
3 x 5² = 75
1 + 3 + 5 + 15 + 25 = 49
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Old 2020-06-18, 12:13   #2
kruoli
 
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What does it have to do with perfect numbers?

Lets have \(p\) prime, not 3. Then the divisors of \(3p^2\) are \(1, 3, p, 3p, p^2, 3p^2\). You want to exclude the last one. Now we sum: \(1 + 3 + p + 3p + p^2 = 4 + 4p + p^2 = (p + 2)^2\).
\(\blacksquare\)
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Old 2020-06-18, 12:19   #3
axn
 
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The sum is called aliquot sum
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Old 2020-06-18, 12:27   #4
drmurat
 
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Quote:
Originally Posted by axn View Post
The sum is called aliquot sum
okay . thanks for information . is it known property of aliquot sum ?
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Old 2020-06-18, 16:48   #5
R.D. Silverman
 
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Quote:
Originally Posted by drmurat View Post
okay . thanks for information . is it known property of aliquot sum ?
simple answer: yes

Your question is totally trivial. It is like asking if 2+2=4 is a "known property".
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Old 2020-06-18, 17:16   #6
LaurV
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Quote:
Originally Posted by kruoli View Post
What does it have to do with perfect numbers?
Elementary my dear Watson... a perfect number is equal to sum of its proper divisors, so you solve the equation \(3p^2 = 4 + 4p + p^2 = (p + 2)^2\), and not only that you found an odd perfect number, which nobody was ever able to find, but moreover, you found something even rarer, an irrational odd perfect number!
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Old 2020-06-18, 17:31   #7
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Misc Math?
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Old 2020-06-18, 17:41   #8
drmurat
 
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Quote:
Originally Posted by R.D. Silverman View Post
simple answer: yes

Your question is totally trivial. It is like asking if 2+2=4 is a "known property".
I saw it in my own calculation . I like it and I share . if you write a link of adocuate site about perfect numbers . I can check property before share .
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Old 2020-06-18, 17:55   #9
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Quote:
Originally Posted by LaurV View Post
Elementary my dear Watson... a perfect number is equal to sum of its proper divisors, so you solve the equation \(3p^2 = 4 + 4p + p^2 = (p + 2)^2\), and not only that you found an odd perfect number, which nobody was ever able to find, but moreover, you found something even rarer, an irrational odd perfect number!
Okay, I agree that it has to do with the sum of its proper divisors, but the solution to the equation given (abbreviated in your post) is simply \(p \in \mathbb R\) (since you were talking about irrational numbers, of couse we could say it is sufficient that \(p \in A\) with \(A\) being a ring (correct me on that, I'm rusty with this)).

Reading again, I think you were sarcastic, but I'm not good at this. Yes, I'd like the odd perfect number problem being solved.
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Old 2020-06-18, 18:16   #10
LaurV
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Quote:
Originally Posted by kruoli View Post
I think you were sarcastic
The sarcasm was not directed towards you. I was just saying (in my own way) that indeed, the story had nothing to do with perfect numbers. In fact, if the OP would have clicked the link from axn, (s)he would have found all the answers, and not needing any other "adocuate" (sic) site about pn's.

Last fiddled with by LaurV on 2020-06-18 at 18:18
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Old 2020-06-18, 18:30   #11
drmurat
 
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Quote:
Originally Posted by LaurV View Post
The sarcasm was not directed towards you. I was just saying (in my own way) that indeed, the story had nothing to do with perfect numbers. In fact, if the OP would have clicked the link from axn, (s)he would have found all the answers, and not needing any other "adocuate" (sic) site about pn's.
it can be sarcastic again but I am making calculations with numbers and I have some results . 6 x 2 , 6 x 3 , 6 x 4 , 6 x 5 ... all is superabundant numbers .
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