Aliquot sequences that start on the integer powers n^i

[garambois]

Until now, the odd bases that we have calculated are often "special" odd numbers : they are prime, primorial ...
For my work in progress, I'm missing some odd bases which are "any" numbers.
I have launched several new bases for a few days, but I will not succeed alone if I want to be able to present this new work to you during my current vacation.

I am missing the following sequences :

- Base 45 up to exponent i = 90, only odd exponents
- Base 75 up to exponent i = 90, only odd exponents
- Base 231 up to exponent i = 70, only odd exponents

If anyone can do any of these calculations, I'm extremely interested ...

As far as I am concerned, I have been working for several days on bases which are primorial numbers and on bases 105 and 15015 which are primorials without the factor 2.
In a few days, you will understand my interest in these bases.

[yoyo]

Here here, here, I take base 45, 75 and 231.

[garambois]

OK, many thanks yoyo !

[Happy5214]

Originally Posted by garambois

Now I understand your idea better.
And I think your idea for the "powers3" html file would bring more clarity to the page and make it easier to exploit the results.
Do you think it would be useful to add the possibility of clicking on the column headers of the "Navigation" table so that only the bases of a single category appear ?
For example, we could click on "Perfect" in the header of the fourth column and that would open the html page that I present below (see "Attached Files").
Thus, one would more easily notice properties specific to perfect numbers.
These html pages for each of the categories are easy for me to generate.
Unless these other pages are not necessary and we can only display the bases of a single category while hiding all the others ?

So you want separate pages for the different categories? I think that would lead to a lot of duplication, as you'd have to repeat the definitions, contributor list, stylesheet, and header info on each page, as well as a few bases. I could probably put it all on one page, add classes to each section tag, put some checkboxes in the navigator, and write a jQuery script to show/hide the sections based on the values of the boxes. I'm not sure how everyone feels about third-party JavaScript libraries (even a FOSS one you could host yourself if you wanted to), but it is significantly easier with jQuery than with plain JS. I'll code up another mock-up and get back to you.

Originally Posted by garambois

On the other hand, I do not understand your comments on the tags.
This is completely outside my area of ​​expertise.
I leave that to the specialists (I also tell myself that the other html pages of my own site must be frankly "disgusting" for a specialist !).

I'm not even that skilled of a web designer. If you look at my personal website, which I think is linked from my profile, it's very rudimentary. I'm just very standards conscious.

Originally Posted by garambois

Small detail : should 6 appear in the "others" column ?

It should not. I copied it to my personal private web server so I could show a family member on my phone (it looks terrible on mobile, by the way), and I did a facepalm when I noticed 6 in the "Others" column, since it's in both the primorial and perfect columns.

[Happy5214]

As promised, the mock-up with the filtering code. It uses the CDN version of jQuery, though you could just as easily replace it with a local copy.

[Happy5214]

The above is superseded by this new mock-up, which corrects an error in the filtering (33 was sorted to the prime filter rather than the other filter), moves the button handling to jQuery, and merges the clearing <div> tag formatting (required due to the floated buttons) into the tables and stat paragraphs. I've also added special indexing to the double-square and perfect number lists, using CSS to add additional text to the indices. You don't have to keep that. It doesn't look as pretty as I thought it would.

[garambois]

Originally Posted by Happy5214

As promised, the mock-up with the filtering code. It uses the CDN version of jQuery, though you could just as easily replace it with a local copy.

You have succeeded in making it possible to display only one category while remaining in a single html file !
This is fantastic !
This time around, the mock-up fits well with the idea we both had at the start.
This new function will certainly make it easier to see certain things, with the growing number of bases.
Thank you very much for this mock-up.

I now think we have to wait a day or two to see if there are other people who want to speak here on this new model.
Please, are there other people who have an opinion (positive or negative) on this mock-up ?
Then, if we validate the idea, I will contact Karsten Bonath, because we will have to integrate all of this in the files that build this html page.
I don't even know if this will be possible ?

Small detail again : it might be better to place the "Display" with their checkbox on the same row, at the top of the column ?

[Happy5214]

Rather than post another full mock-up, just add the following line below line 19 of powers5.html:

nav td {vertical-align: top;}

I'm glad you like it. And I really hope this can be automated.

[Happy5214]

I went ahead and posted another mock-up anyway, since I also found a way to make the double-square list much prettier.

[garambois]

Personally, it is version N ° 6 that I prefer.

[EdH]

I might have mentioned a couple of these before, but basically, all cells of bases 450 and 578 through exponent 50 are now green (terminated).