Talk:Untouchable number

Formula?

is there any formula to calculate untouchable number? —Preceding unsigned comment added by 60.51.172.69 (talk • contribs) 04:27, 12 February 2008

So what about an explanation of what is so significant about an untouchable number for non-maths geniuses? I mean really what is the point?? Apart from wasting the time and budgets of maths departments? I mean who really needs to know this? Like it needs to have a sentence like

"Untouchable numbers are used in (insert field of study) for calculating (insert contribution to human knowledge)"

Because obviously it must be important to earn such a cool name... I mean as the article stands right now I am left to imagine that these are the Elliot Nesses of the number world. While lesser numbers are just a number, untouchable stand protecting (number-) order; less susceptible to bribes standing up to mobsters (or at very least their accountants).... but that probably isn't the reason why they are called untouchable. Or was it these numbers that Ghandi was fighting for? The poor, the dejected and downtrodden untouchables? —Preceding unsigned comment added by 122.27.1.134 (talk • contribs)

This isn't my field and I could be wrong, but I would be quite surprised to learn that these numbers were useful for anything whatsoever. Algebraist 19:37, 17 May 2008 (UTC)

They are in some way related to prime numbers, if vaguely. I can't really get deeper into it since I don't know a lot about them. Even so, the article doesn't appear to be for non-math geniuses (if you're some other kind of genius you wouldn't have any use for untouchable numbers).

I really don't understand this...

"For example, the number 4 is not untouchable as it can be made up of the sum of the proper divisors of 9, i.e. 1 & 3. The number 5 is untouchable as a similar thing cannot be done."

If the proper divisors of 9 are 1 and 3 (and I guess an implied 9)... then couldn't we use 6. The proper divisors of 6 are 1, 2, 3, and 6... 2 + 3 = 5. So the sums of the Proper Divisor of 6 is 5. Which would conflict with the statement that 5 is an untouchable number, if the first statement is fact as well. Unless I'm completely misunderstanding this entry... which means it needs to be reworked. —Preceding unsigned comment added by 98.225.216.197 (talk) 14:22, 28 May 2009 (UTC)

5 cannot be used, since there is no positive integer where the sum of the divisors of that integer is 5. The sum of the divisors of 6 is 1 + 2 + 3 + 6 = 12. So that won't do. The article mentions that the sum of all the divisors has to be used -- not just the ones we like -- and the article is just fine (on that point). If we could just pick the divisors we wanted, there wouldn't be any untouchable numbers, since an untouchable number would then be a positive integer which could not be expressed as a sum of positive integers (which they all, except 1, can).

I found that explanation very helpful. You might want to incorporate that into the article. I didn't see why 5 was untouchable. Once in a while I say something nice, and you are today's winner! —Preceding unsigned comment added by 69.171.176.218 (talk) 16:50, 28 October 2010 (UTC)

96 and 120

They're listed as untouchable numbers, but 96 is the sum of 69's divisors, and 120 is the sum of 95's divisors. Shouldn't they be removed? Avengingbandit 01:54, 26 September 2021 (UTC)

Nevermind; I didn't see that the number itself does not count as a divisor for this purpose. Avengingbandit 01:58, 26 September 2021 (UTC)