Talk:Jordan-Pólya numbers: Difference between revisions

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Latest revision as of 17:38, 11 June 2023

Isn't that like N-smooth_numbers using n! instead of primes?

In N-smooth numbers one can change p1..pn by 2! to n!
I think , only using 2!,3!,5!,..pn! is sufficient. 4! = (2!)^2*3!, 6! = 5!*3!... so no extra numbers will be created.

7213895789838336 =(4!)^8 * (2!)^16 == ((2!)^2 *(3!))^8 * (2!)^16 = (2!)^32*(3!)^8

Horst (talk) 08:48, 9 June 2023 (UTC)

There may, of course, be more than one way to decompose a J-P number into a product of factorials but the idea is to choose the way which uses the largest factorials and present these in highest to lowest order. I've added a sentence to the task description to try and clarify this. --PureFox (talk) 09:57, 9 June 2023 (UTC)

I believe (bicbw) there is no way to make 439,378,587,648,000 = 14! * 7! with only prime factorials. --Petelomax (talk) 02:53, 10 June 2023 (UTC)

Yes, your right.14! = 13!*2*7 2= 2! but no way to get a lonely 7. Of course there 16!= 2!^4 * 15! . To much work for to less advantage --Horst (talk) 16:28, 11 June 2023 (UTC)

Factoring the 1050th number

The 1050th jp number is 139,345,920,000. It factors as 7! * 5!^3 * 2!^4 or 8! * 5!^3 * 2! but the ~~Phix~~/Julia/Wren entries are not getting that. Update: new algorithm posted, however my faffing about with prime powers is probably not the point, one-at-a-time/less greedy probably is. --Petelomax (talk) 05:31, 10 June 2023 (UTC)

Well spotted! Rather than translate yours, I've modified the decomposition algorithm I was using for both Wren versions using recursion and it now seems to be working OK. --PureFox (talk) 11:31, 10 June 2023 (UTC)

@@ Line 9: / Line 9: @@
 :There may, of course, be more than one way to decompose a J-P number into a product of factorials but the idea is to choose the way which uses the largest factorials and present these in highest to lowest order. I've added a sentence to the task description to try and clarify this. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 09:57, 9 June 2023 (UTC)
 :I believe (bicbw) there is no way to make 439,378,587,648,000 = 14! * 7! with only prime factorials. --[[User:Petelomax|Petelomax]] ([[User talk:Petelomax|talk]]) 02:53, 10 June 2023 (UTC)
+:Yes, your right.14! = 13!*2*7  2= 2! but no way to get a lonely 7. Of course there 16!= 2!^4 * 15! . To much work for to less advantage  --[[User:Horst|Horst]] ([[User talk:Horst|talk]]) 16:28, 11 June 2023 (UTC)
 == Factoring the 1050th number ==
-The 1050th jp number is 139,345,920,000. One and I suspect the only possible factorisation is 7! * 5!^3 * 2!^4, but the Phix/Julia/Wren entries are not getting that. I have thought of a better strategy, based on the prime powers, but it is not straightforward and would naturally produce the ''lowest'' factorials - I ''think'' I might  have just thought of a way to convert that to the highest factorials... In the meantime, some examples:
+The 1050th jp number is 139,345,920,000. It factors as 7! * 5!^3 * 2!^4 or 8! * 5!^3 * 2! but the <del>Phix</del>/Julia/Wren entries are not getting that. Update: new algorithm posted, however my faffing about with prime powers is probably not the point, one-at-a-time/less greedy probably is. --[[User:Petelomax|Petelomax]] ([[User talk:Petelomax|talk]]) 05:31, 10 June 2023 (UTC)
-<pre>
+:Well spotted! Rather than translate yours, I've modified the decomposition algorithm I was using for both Wren versions using recursion and it now seems to be working OK. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 11:31, 10 June 2023 (UTC)
-,160 = 6! * 2!^7, or
-,160 = 5! * 3! * 2!^7
-,345,885,696 = 4!^7 * 2!^2, or
-,345,885,696 = 3!^7 * 2!^16
-,345,920,000 = 7! * 5!^3 * 2!^4 (only one?)
-,345,885,696 = 4!^7 * 2!^2, or
-,345,885,696 = 3!^7 * 2!^16
-,775,731,200 = 6! * 5! * 2!^23, or
-,775,731,200 = 5!^2 * 3! * 2!^23
-,784,472,371,200 = 6!^2 * 4!^2 * 2!^15, or
-,784,472,371,200 = 5!^2 * 3!^4 * 2!^19
-,378,587,648,000 = 14! * 7! (only one?)
-,213,895,789,838,336 = 4!^8 * 2!^16, or
-,213,895,789,838,336 = 3!^8 * 2!^32
-</pre>
-There are probably only a few ways to do each, maybe show them all? --[[User:Petelomax|Petelomax]] ([[User talk:Petelomax|talk]]) 23:52, 9 June 2023 (UTC)