Talk:Colossally abundant number

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Aren't these the same as Superior highly composite numbers????Scythe33 14:44, 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 18:31 (UTC)

See my remarks in the discussion page for superior highly composite numbers. They use different divisor functions; Scythe33's change to the definition is wrong (and would be satifsied by all superabundant numbers). DPJ, 16 Aug 2005 6:26 UTC

W.r.t. "All colossally abundant numbers are Harshad numbers." is this true only in base 10 (for the Harshad definition)? Rycanada 18:57, 16 February 2006 (UTC)

Relation to the Riemann hypothesis. How are they related - This is actually a question of interest. Please put this relation explicitely.

f the RH is false, a colossally abundant number will be a counterexample (probably the first counterexample; it's 'obvious' that the first counterexample must be a superabundant number). See [1]. CRGreathouse 04:01, 15 July 2006 (UTC)

I don't understand this sentence. To me a counterexample to the Riemann hypothesis is some non-integer complex number s such that z(s) = 0. Surely you must refer to some function f : N -> {0,1} which is constantly 0 if RH holds, and your "first counterexample" must be the first n such that f(n) = 1. What f are you talking about ? (A quick parse of the article your reference yields me no hint of such an f.) --FvdP (talk) 19:56, 5 December 2007 (UTC) Doh. The answer is in the article. --FvdP (talk) 20:03, 5 December 2007 (UTC)