Re: Weird Numbers (#57)


#1

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


#2

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/njas/sequences/eisA.cgi?Anum=A006037

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?


#3

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


#4

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


#5

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


#6

Nate wrote:

Very confused,

-Nate

erm, if 2 is a divisor 836/2=418 should also be, hmm?

get some sleep :slight_smile:

(and you missed some more: 1, 4, 38, 44, 76)

cheers

Simon


#7

Ah ha. That’s exactly what I was looking for.

Thanks!


#8

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.


#9

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


#10

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


#11

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… :wink:

James Edward G. II


#12

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… :wink:

James Edward G. II