Talk:Amicable numbers

Old comments
"Also, every known pair shares at least one common factor": Isn't this obvious as 1 is always a common factor, or should it be at least two common factors? A nice homepage can be found under http://www.shyamsundergupta.com/amicable.htm Renger van Nieuwkoop 09:54, 31 January 2007 (UTC)

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This article is very biased towards the achievements of Arab mathematicians. I'm not saying that they didn't contribute a lot but it just reads like a defence of their contribtion rather than a objective article about the subject and its history. I would put up a banner at the top of the page saying that the neuterality of this article is disputed but I don't know how to do that. —Preceding unsigned comment added by 81.144.251.46 (talk) 14:26, 18 December 2007 (UTC)

--- There are, in particular, no proper references to specific pairs found by e.g. Ibn Qurra's formula. The article referenced in the linked article, https://www.ams.org/journals/mcom/1986-46-173/S0025-5718-1986-0815849-1/S0025-5718-1986-0815849-1.pdf, does have some better references to secondary literature on this score.

On a separate note, there doesn't seem to be any contemporary evidence that Pythagoras cared about these. — Preceding unsigned comment added by 96.230.129.52 (talk) 15:59, 25 January 2021 (UTC)

Code
I'm curious about the code and "pseudocode" in this article. This code doesn't add anything significant to the content: the algorithms are completely obvious from the definition of amicable number. Can anyone give a supporting argument for their presence? If not, I'll just go ahead and remove them. Cheers, Doctormatt (talk) 00:29, 18 June 2008 (UTC)
 * They've been deleted.--RDBury (talk) 16:55, 6 December 2008 (UTC)

Recent additions
I added some of the information from Mathworld and promoted to article to Start class. There is much more information that could be added from this source as well. The article on Thâbit's rule could also be expanded, however the article on Euler's rule has nothing new and could probably be merged with this one. Given that the topic did rate an article in the 1911 Encyclopædia Britannica and is the topic of several articles in Mathworld, and because of it's historical importance, I also raised the priority to Mid.--RDBury (talk) 17:14, 6 December 2008 (UTC)

Paganini
Paganini is said to have made the discovery in 1860 and 1866. No doubt, his work took some time. —Preceding unsigned comment added by 86.137.170.8 (talk) 11:27, 18 August 2009 (UTC) Who is "B. Nicolo I. Paganini"? This is clearly not the violinist and composer Niccolò Paganini, who died in 1840. Jperrylsu (talk) 22:00, 10 February 2014 (UTC)

Gap in the definition?
The definition given seems to be the usual one, but seems to have a problem with primes. The sum of the proper divisors of any prime is 1 so all primes would be amicable, but they are not usually considered so (otherwise the first two sociable numbers would be 2 and 3). Should primes be specifically excluded in the definition? Digitig (talk) 15:10, 11 November 2011 (UTC)


 * How so? The sum of the proper divisors of 7 is 1, but the sum of the proper divisors of 1 is not 7, therefore 7 is not an amicable number. None of the primes are, without needing to specifically exclude them. Owen&times;  &#9742;  15:22, 11 November 2011 (UTC)
 * Yes, sorry, brain fade. Should I remove the question, or leave it up for my perpetual embarrassment?
 * Digitig (talk) 15:29, 11 November 2011 (UTC)
 * Don't worry about it, we all have such moments. Owen&times; &#9742;  16:36, 11 November 2011 (UTC)
 * But see also Ruth–Aaron pair and Friendly number - you may have been thinking of one of those. Owen&times; &#9742;  16:51, 11 November 2011 (UTC)

Significance
What is the significance of amicable numbers? Do they have any practical applications? Do they reveal any underlying science? Or are they just a trivial quirk of mathematics? — Preceding unsigned comment added by 79.235.254.69 (talk) 09:52, 20 June 2019 (UTC) I came to this article with the express hope that it could enlighten me in any way why I would care about these numbers. I see there is a distributed project to find them on boinc but why would anyone care to donate cpu cycles to such a project if the numbers themselves don't have any practical uses? (As a counter example, another distributed search for Optimal Golomb Rulers at least claims the numbers are useful for antenna arrangements.) — Preceding unsigned comment added by 24.156.255.250 (talk) 22:55, 10 March 2020 (UTC)


 * No one said that they needed a practical use. It is to discover how the world is. Bubba73 You talkin' to me? 02:29, 11 March 2020 (UTC)