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 2020-06-18, 11:56 #1 drmurat   "murat" May 2020 turkey 658 Posts 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
 2020-06-18, 12:13 #2 kruoli     "Oliver" Sep 2017 Porta Westfalica, DE 22·73 Posts 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: $$1 + 3 + p + 3p + p^2 = 4 + 4p + p^2 = (p + 2)^2$$. $$\blacksquare$$
 2020-06-18, 12:19 #3 axn     Jun 2003 10010010101012 Posts The sum is called aliquot sum
2020-06-18, 12:27   #4
drmurat

"murat"
May 2020
turkey

53 Posts

Quote:
 Originally Posted by axn The sum is called aliquot sum
okay . thanks for information . is it known property of aliquot sum ?

2020-06-18, 16:48   #5
R.D. Silverman

Nov 2003

1D2416 Posts

Quote:
 Originally Posted by drmurat okay . thanks for information . is it known property of aliquot sum ?

Your question is totally trivial. It is like asking if 2+2=4 is a "known property".

2020-06-18, 17:16   #6
LaurV
Romulan Interpreter

Jun 2011
Thailand

2×11×397 Posts

Quote:
 Originally Posted by kruoli 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!

 2020-06-18, 17:31 #7 kriesel     "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 3×13×113 Posts Misc Math?
2020-06-18, 17:41   #8
drmurat

"murat"
May 2020
turkey

53 Posts

Quote:
 Originally Posted by R.D. Silverman 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 .

2020-06-18, 17:55   #9
kruoli

"Oliver"
Sep 2017
Porta Westfalica, DE

22·73 Posts

Quote:
 Originally Posted by LaurV 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.

2020-06-18, 18:16   #10
LaurV
Romulan Interpreter

Jun 2011
Thailand

100010000111102 Posts

Quote:
 Originally Posted by kruoli 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

2020-06-18, 18:30   #11
drmurat

"murat"
May 2020
turkey

658 Posts

Quote:
 Originally Posted by LaurV 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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