Talk:Multiply perfect number

Example?[edit]

To be honest I don't understand much of this explanation. It would be helpful if someone could illustrate 'multiply perfect numbers' with an example. --Steerpike 10:41, 27 March 2006 (UTC)[reply]

I have added an example.[1] PrimeHunter (talk) 13:26, 31 March 2008 (UTC)[reply]

I regard myself as a bit of a mathematician but I found the explanations completely incomprehensible. Surely a casual reader would not have a clue. I'm sure that I can work out what they mean and when I do I'll rewrite it in English.OrewaTel (talk) 00:25, 20 May 2020 (UTC)[reply]

I've added an example. Bubba73 ^{You talkin' to me?} 00:45, 20 May 2020 (UTC)[reply]

Known values?[edit]

"As of July 2004, k-perfect numbers are known for each value of k up to 11." This needs some clarification (at least one k-perfect number was found for k=1-11? All k-perfect numbers known for 1-11?) and also a citation. The linked [mpn page](http://wwwhomes.uni-bielefeld.de/achim/mpn.html) seems to indicate that we don't even know all MPNs <= 7, so I also added a cite needed template. — Preceding unsigned comment added by Xodarap00 (talk • contribs) 13:28, 20 March 2014 (UTC)[reply]

We do not know all the multiply perfect numbers. We do not even know whether there are finitely many. We do know the 6 smallest triperfect numbers and it is conjectured that there are no more. But there is no proof.OrewaTel (talk) 00:21, 20 May 2020 (UTC)[reply]

Known 11-perfect numbers[edit]

According to the multiply perfect numbers website Multiply Perfect Numbers, there is only one known 11-perfect number whose prime factorization starts as:

2⁴⁶⁸ 3¹⁴⁰ 5⁶⁶ 7⁴⁹ 11⁴⁰ 13³¹ 17¹¹ 19¹² 23⁹ 29⁷ 31¹¹ 37⁸ 41⁵ 43³ 47³ 53⁴ 59³ 61² 67⁴ 71⁴ 73³ 79 83² 89 97⁴ 101⁴ 103³ 109³….

This is the only 11-perfect number that we know of so far. I really wished for a larger list of 11-perfect numbers. I wished that we know of more positive integers n that satisfy σ(n) = 11n. That number was discovered back in March 2001 by George Woltman, more than 20 years ago. So can you try to discover an 11-perfect number on your own?

If you are a Wikipedia user who is interested in numbers, please try to discover an 11-perfect number on your own. The prime factorization of an example is provided on the article in the table where the first column of the row says "11". You can look at the prime factorizations of other multiply perfect numbers (σ(n)/n is an integer < 11) while you are trying to discover another 11-perfect number. Below are the links:

[2] (6-perfect numbers)

[3] (7-perfect numbers)

[4] (8-perfect numbers)

[5] (9-perfect numbers)

[6] (10-perfect numbers)

To look at the prime factorizations of the numbers in the lists above, you can copy a number in any of the tables above and paste it into an integer factorization program called https://www.alpertron.com.ar/ECM.HTM. You can copy the numbers one by one and paste it into the integer factorization calculator and click "Factor", and this will give you the prime factorization of the number. You can also import a list of numbers into the calculator and click "Factor", and this will give you the prime factorizations of multiple n-perfect numbers. To do this, copy and paste multiple numbers in the list into the calculator. However, this will take a very long time to factor all of the numbers in the list if you copy and paste all of the 9- or 10-perfect numbers into the calculator, since many of the numbers take a wasteful amount of time to fully factor.

After you looked at the prime factorizations of the known multiply perfect numbers, you might be familiar with all of the prime factorizations of the known multiply perfect numbers. Become a mathematician and try to discover an 11-perfect number on a supercomputer.

I really wish for more 11-perfect numbers, so if you are a Wikipedia user who is interested in numbers and you are reading this, please try to discover an 11-perfect number. Fomfeider (talk) 16:32, 28 October 2021 (UTC)[reply]

Are you able to discover an 11-perfect number on your own? Fomfeider (talk) 15:06, 1 November 2021 (UTC)[reply]

You can certainly try to find more, but ut isn't easy. Bubba73 ^{You talkin' to me?} 21:13, 3 November 2021 (UTC)[reply]

@Bubba73: But how can I find one, particularly what power of 2 can I use for my 11-perfect number that I am trying to find? The one that we know has 2 to the power of 468, but what power of 2 can I use in my number? Fomfeider (talk) 13:01, 4 November 2021 (UTC)[reply]

@Fomfeider: Uh, how did I get tagged when I've never been on this page before? Seasider53 (talk) 13:05, 4 November 2021 (UTC)[reply]

@Seasider53: You mean, the pages with the URL www.bitman.name? There is a list of multiply perfect numbers on those pages. Fomfeider (talk) 13:08, 4 November 2021 (UTC)[reply]

@Anita5192: Please try to discover an 11-multiperfect number. Fomfeider (talk) 16:03, 16 November 2021 (UTC)[reply]

Is this correct? "a number is thus perfect if and only if it is 2-perfect."[edit]

I don't think it can be right, but maybe I'm misunderstanding it. I mean, 6 is perfect, but its divisors do not sum to 12, so it is not 2-perfect. Joe in Australia (talk) 01:14, 4 September 2022 (UTC)[reply]

@Joe in Australia: The statement is correct. The divisors include the number itself. n is perfect if and only if the divisors exluding n have sume n. Including n makes the sum 2n which defines a 2-perfect number. PrimeHunter (talk) 06:47, 4 September 2022 (UTC)[reply]