If I got I right, 70 would be such a number. (I hope this is no spoiler) divisors = [1, 2, 5, 7, 10, 14, 35] sum = 74 no combination of the divisors adds up to 70 cheers Simon

on 2005-12-02 16:59

on 2005-12-02 17:32

>please give an example of such a number. 70,836,4030,5830,7192,7912,9272,10430,10570,10792,10990, 11410,11690,12110,12530,12670,13370,13510,13790,13930,14770, 15610,15890,16030,16310,16730,16870,17272,17570,17990,18410, 18830,18970,19390,19670 On-Line Encyclopedia of Integer Sequences! http://www.research.att.com/cgi-bin/access.cgi/as/... See Also: http://en.wikipedia.org/wiki/Weird_number http://mathworld.wolfram.com/WeirdNumber.html I would like to see an iterator in Ruby that took as one of its arguments the On-Line Encyclopedia of Integer Sequences identifier (A006037). And also an iterator in Ruby for the Combinatorial Object Server: Combinatorial Object Server http://www.theory.cs.uvic.ca/~cos/cos.html Is that possible in Ruby?

on 2005-12-02 17:56

If you download the Mathematica notebook file for "Weird Number" from this site: http://mathworld.wolfram.com/WeirdNumber.html You can convert the notebook file to pdf with this utility: http://library.wolfram.com/Explore/Publishing/NBtoPDF.jsp

on 2005-12-04 01:25

Dan D. wrote: > >please give an example of such a number. > > 70,836,4030,5830,7192,7912,9272,10430,10570,10792,10990, > 11410,11690,12110,12530,12670,13370,13510,13790,13930,14770, > 15610,15890,16030,16310,16730,16870,17272,17570,17990,18410, > 18830,18970,19390,19670 > I can see how 70 is a "weird number" (divisors 2 + 5 + 7 + 10 + 14 + 35 = 74 and no subset adds up to 70), but can someone explain to me how 836 is considered "weird"? 2 + 11 + 19 + 22 + 38 + 209 = 301 Am I missing a divisor, because last time I checked 301 < 836. When I factor 836, I come up with 2 * 2 * 11 * 19 = 836. Is this just one of those cases where the internet is *wrong*? Very confused, -Nate

on 2005-12-04 01:29

```
On Dec 3, 2005, at 5:22 PM, Nate wrote:
> When I factor 836, I come up with 2 * 2 * 11 * 19 = 836.
You're using the same factor twice in there. That doesn't seem right...
James Edward G. II
```

on 2005-12-04 01:33

Nate wrote: > > Very confused, > > -Nate erm, if 2 is a divisor 836/2=418 should also be, hmm? get some sleep :) (and you missed some more: 1, 4, 38, 44, 76) cheers Simon

on 2005-12-04 01:45

James Edward G. II wrote: > On Dec 3, 2005, at 5:22 PM, Nate wrote: > > > When I factor 836, I come up with 2 * 2 * 11 * 19 = 836. > > You're using the same factor twice in there. That doesn't seem right... > True, the only factors of 836 are 2, 11, and 19. I just meant to point out that those are definitely the only factors because 2^2 * 11^1 * 19^1 = 836. That said, does 836 have any other divisors besides 2, 11, 19, 22, 38, and 209? I don't see how it could, but I would love to be proved wrong. Mostly I just want to know if the list posted previously is accurate or not.

on 2005-12-04 02:17

On 12/4/05, Nathan <removed_email_address@domain.invalid> wrote: > > True, the only factors of 836 are 2, 11, and 19. I just meant to point > out that those are definitely the only factors because 2^2 * 11^1 * > 19^1 = 836. That said, does 836 have any other divisors besides 2, 11, > 19, 22, 38, and 209? I don't see how it could, but I would love to be > proved wrong. irb(main):001:0> (1..836).select{|d| 836 % d == 0} => [1, 2, 4, 11, 19, 22, 38, 44, 76, 209, 418, 836] > Mostly I just want to know if the list posted previously is accurate or > not. I think it is. Paolo

on 2005-12-04 02:38

Paolo C. wrote: > On 12/4/05, Nathan <removed_email_address@domain.invalid> wrote: > > irb(main):001:0> (1..836).select{|d| 836 % d == 0} > => [1, 2, 4, 11, 19, 22, 38, 44, 76, 209, 418, 836] Simon's right. I definitely need more sleep. Cheers, -Nathan

on 2005-12-04 17:51

On Dec 2, 2005, at 9:31 AM, Dan D. wrote: > I would like to see an iterator in Ruby that took as one of its > arguments the On-Line Encyclopedia of Integer Sequences identifier > (A006037). And also an iterator in Ruby for the Combinatorial > Object Server: > > Combinatorial Object Server > http://www.theory.cs.uvic.ca/~cos/cos.html > > Is that possible in Ruby? You bet. Use the openuri library to grab the page, parse out what you need, and yield results. It's not even hard. Give it a try and you'll learn a lot about Ruby... ;) James Edward G. II

on 2005-12-04 18:40

I am not talking about screen scraping bits and pieces of information off web sites but rather having a library of combinatorial iterators wrapped up in classes: Combinations, Permutations, ... Debruijn Sequences. Ruby blocks & yield statements would be a great way to process each element of the combinatorial structure seperating the problems of 1) generating the next element of combinatorial structure from 2) processing each element of the combinatorial structure. James Edward G. II <removed_email_address@domain.invalid> wrote: On Dec 2, 2005, at 9:31 AM, Dan D. wrote: > I would like to see an iterator in Ruby that took as one of its > arguments the On-Line Encyclopedia of Integer Sequences identifier > (A006037). And also an iterator in Ruby for the Combinatorial > Object Server: > > Combinatorial Object Server > http://www.theory.cs.uvic.ca/~cos/cos.html > > Is that possible in Ruby? You bet. Use the openuri library to grab the page, parse out what you need, and yield results. It's not even hard. Give it a try and you'll learn a lot about Ruby... ;) James Edward G. II