Talk:Superior highly composite number

message: This:
    In mathematics, a superior highly composite number is a natural number which has more divisors than any other number scaled relative to the number itself
should be defined. Wlod (talk) 07:01, 22 October 2014 (UTC)
replies: text: It was originally a lose description after the definition  but then the lead was restructured so it sounded like the definition itself while the actual definition sounded like a derived property. I don't have time to improve it now. PrimeHunter (talk) 12:36, 22 October 2014 (UTC)
thread_title:  Definition? 

message: I obviously did not work this out by hand. :-) I did this for putting in the article, but they quickly became walls of text so enormous that I truncated it at the tenth SHCN (720720) – which already has every integer from 1 to 16 as a divisor!
see: /Factors
A neat illustration of just how superior highly composite these numbers are, I guess, but an impenetrable wall of text for the last few. Double sharp (talk) 14:44, 26 February 2015 (UTC)
thread_title:  Factors of the first seventeen SHCNs 

message: I tweaked the opening statement... In mathematics, a superior highly composite number or convergence point is a natural number which has more divisors than any other number scaled relative to some positive power of the number itself. It is a stronger restriction than that of a highly composite number, which is defined as having more divisors than any smaller positive integer. 50.245.89.150 (talk) 01:38, 18 July 2019 (UTC)
thread_title:  Superior highly composite number or Convergence Point 

message: I believe it needs to be reworded in a way that's more intuitive than how it is now. I made the (now reverted) change because I believed "when adjusted for magnitude" seemed much easier to understand than "scaled relative to some positive power of the number itself". For example, when I first read this, I thought "the number itself" was referring to the natural number in question, not just "any" number scaled relative to the same power of "any" number. What about a middle ground between my change and how it is now? Avengingbandit 20:14, 18 August 2021 (UTC)
replies: text: Now it gives the definition in words although it may be hard to understand and require some interpretation. "adjusted for magnitude" is not a definition without saying how the adjustment is made, which is impossible to guess in this case where the adjustment method is complicated and invented specificially for these numbers. Apart from being vague, I also think "adjusted for magnitude" is misleading because it would normally mean the same adjustment is made for all superior highly composite numbers. If that was the case then there could only be one number with more divisors than any other number "adjusted for magnitude". If we don't want a complicated definition and cannot make a simple definition then we shouldn't give something which sounds like a definition but isn't, and is misleading. How about: "a superior highly composite number is a natural number which has more divisors than any other number when adjusted for magnitude in a certain way which is a little different for each superior highly composite number." It may sound vague and clunky but it's correct. "in a certain way" makes it clear that this is not the actual definition, and "a little different for each superior highly composite number" explains how there could be more than one with more divisors than any other number. Without this part, many readers will probably think there must be an error in the sentence, e.g. that it should have said "more divisors than any smaller number". PrimeHunter (talk) 01:27, 19 August 2021 (UTC)
replies: text:  The way you worded it makes it hard for me to tell if you're seriously suggesting "in a certain way which is a little different" wording; I would not be opposed to that if you are. Another suggestion of mine would be "more divisors than any other number when divided by some positive power of itself"? Replaces "scaled" with "divided" and "the number itself" with just "itself". You may not find that necessary but as a fellow reader I'd like to be able to clearly and unambiguously understand what I'm reading. I wouldn't see anything wrong with that. Avengingbandit 02:12, 19 August 2021 (UTC)
replies: text:  That sounds good. PrimeHunter (talk) 01:28, 20 August 2021 (UTC)
thread_title:  Wording of the beginning sentence