Talk:Superior highly composite number

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Aren't these the same thing as Colossally abundant numbers???? The articles should be combined if so.Scythe33 14:35, 14 Jun 2005 (UTC)

I'm not an expert, but it appears they are different. In the definition of superior highly composite number, the exponent is required to be > 0, whereas in the definition of colossally abundant number, the exponent is required to be > 1, so every colossally abundant number is superior highly composite, but not conversely. See also the links to the encyclopedia of integer sequences. Revolver 6 July 2005 18:32 (UTC)
They're two completely different things. Superior highly composite numbers are defined in terms of number of divisors (d function); colossally abundant numbers are defined in terms of sum of divisors (sigma function). DPJ, 16 Aug 2005 6:13 UTC

Further research shows that the definition is wrong. (At 14:27, 14 June 2005 Scythe33 changed the definition; the article was right the first time.) According to the definition supplied by Scythe33, every highly composite number would qualify. DPJ, 16 Aug 2005 6:21 UTC

Why isn't n=1 included as a superior highly composite number? Putting ε = 1, we get d(k)/k \le 1 = d(1)/1, which suggests that 1 is a superior highly composite number. DRLB 14:56, 19 October 2006 (UTC)

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