20210304, 09:08  #936  
"Garambois JeanLuc"
Oct 2011
France
3×5×37 Posts 
Quote:
I will probably put the page on my website as shown in post # 925, unless you still make some changes in the layout or in the tags, area where I don't understand much. I will also have less time in the next few days, because unfortunately my vacation is going to end. I can always edit the page later. 

20210304, 09:24  #937  
"Garambois JeanLuc"
Oct 2011
France
3·5·37 Posts 
Quote:
Thank you for this demonstration attempt ! Me, I am focusing on the end of remark 2 of post #921. OK, now the calculations have been done for base 38. But why do we have nothing for bases 6, 12, 24, 30, 72 ...? These are bases which have the factor 3 in their decomposition. But there are others who have the factor 3 and who have something: 18, 42, 882 ... I look at the data over and over again ! 

20210304, 11:54  #938  
"Alexander"
Nov 2008
The Alamo City
574_{10} Posts 
Quote:
PS Regarding above, I did end up finding the formulas, but still couldn't complete the inductive proof. I'll post the formulas here if anyone wants to try their hand at it: Code:
x = ((19^(12*(n+1)+1))((19^(12*n+1))))/18 y = 2^(12*(n+1)+1)2^(12*n+1) z = (((19^(12*(n+1)+1))((19^(12*n+1))))/18) * (2^(12*(n+1))2) w = (2^(12*(n+1)+1)2^(12*n+1)) * (((19^((12*n)+1))19)/18) v = 2^(12*(n+1)) * (((19^(12*(n+1)))((19^(12*n+1))))/18) prev = 2^(12*n) * 19^(12*n) old = <previous sum> new = old+prev+x+y+z+w+v Last fiddled with by Happy5214 on 20210304 at 12:00 Reason: Adding formulas for 38^12n 

20210304, 13:58  #939 
Sep 2008
Kansas
CF3_{16} Posts 
In keeping with the spirit of investigating base 2*p, next up is base 46.
Preliminary results show a similar phenomena. Additionally, 46^6n shows an abundance of (3 * 5 * 7) along with 46^12n (3 * 5 * 7 * 13) to advance the sequence. 
20210304, 15:45  #940  
Aug 2020
2×3^{2} Posts 
Quote:


20210304, 18:51  #941  
"Garambois JeanLuc"
Oct 2011
France
3·5·37 Posts 
Quote:
Thanks a lot for your help ! I will try to modify the html code like in your example. But I'm running out of time. I think it takes hours of work to rearrange everything like in your example. I hope I am wrong. I don't know when I will be able to publish the page or both pages if I separate the two posts. I will keep you posted... 

20210304, 19:03  #942  
"Garambois JeanLuc"
Oct 2011
France
3·5·37 Posts 
Quote:
OK, seen. Thanks for the base 46. You talk about an abundance of (3 * 5 * 7), didn't you want to write (3^3 * 5 * 7) instead ? 

20210304, 21:57  #944 
Sep 2008
Kansas
3·5·13·17 Posts 

20210304, 22:09  #945  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
5,857 Posts 
Quote:


20210304, 22:22  #946 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
5,857 Posts 
Assuming no factors below 1e20 then the maximum abundance contribution of the C353 can be upper bounded by ((1e20+1)/1e20)^(floor(353/20))= (1+1e20)^17= 1.00000000000000000017 or there about.

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