Talk:Abundant number

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Mathematics rating:	Start Class	Low Priority	Field: Number theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. needs:motivation, organisation, and history--Cronholm144 02:30, 13 May 2007 (UTC)

proper multiple? -- Cimon Avaro on a pogo-stick 13:51, Sep 19, 2003 (UTC)

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"open interval" termonology used with closed interval (brackets) The article mentions an "open interval" (and even provides a link with example usage) but uses brackets instead of parenthesis. Unfortunately, I am unsure whether it is supposed to actually be a "closed interval" (which would match the notation), an "open interval" (in which case, I believe the bounds should be marked with parenthesis and not square brackets), or I am simply wrong. ampre 06:17, 1 May 2004 (UTC)

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According to this page, Nicomachus had a different definition for abundant numbers: he "only required that σ(n) exceeds n". As σ(n) is the sum of all divisors of n including n itself, σ(n)>n for all positive integers larger than 1. I don't think this was what he meant, so I have removed the alternative definition from the article. Eugene van der Pijll 23:02, 17 Mar 2005 (UTC)

[edit] Mathworld / Wikipedia definitions of "abundance"

This article defines an “abundant number” as an integer whose proper divisors add up to twice the number itself. It gives this example for the abundant number 24: “1, 2, 3, 4, 6, 8, 12 and 24, whose sum is 60. Because 60 is more than 2 × 24, the number 24 is abundant. Its abundance is 60 − 2 × 24 = 12.

But in one of the external links cited (Mathworld) author Eric W. Weisstein says there that abundant numbers need only be greater than the sum of the proper divisors of that number, although he does not allow the number to be counted as a divisor of itself. Of course, the two defs are equivalent, but it is a bit fiddly. Would suggest Wikipedia fall in line with Matchworld definition, because it is simpler, and also because people are used to factors of 1 and the number itself being excluded when primes are being defined Myles325a 09:50, 6 March 2007 (UTC)

[edit] amicable numbers

Congrats to all on the beautiful layout of these articles, and the cross-referencing on the front page. Would suggest adding "Amicable Numbers" to thio list.Myles325a 09:53, 6 March 2007 (UTC)