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 2015-11-22, 10:03 #1 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
 2015-11-28, 10:40 #2 davar55     May 2004 New York City 10000100010002 Posts Just starting to read your refreshing work. Two paragraphs in and it looks and reads clean.
 2015-11-28, 11:04 #3 davar55     May 2004 New York City 23×232 Posts In section 2: where you have Code: prod of a-sub-i + 1 it should perhaps read Code: prod of (a-sub-i + 1) Do you want or need this type of comment for minor points or typos?
2015-11-28, 11:17   #4
Dubslow
Basketry That Evening!

"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

160658 Posts

Quote:
 Originally Posted by davar55 Just starting to read your refreshing work. Two paragraphs in and it looks and reads clean.
Note that the rechenkraft version is currently not quite up to date with some typo fixes, a couple of incorrect statements removed, and of course the lack of the proof axn provided. Use this for now.

Quote:
 Originally Posted by davar55 In section 2: where you have Code: prod of a-sub-i + 1 it should perhaps read Code: prod of (a-sub-i + 1) Do you want or need this type of comment for minor points or typos?

Please. Though perhaps the thread in the aliquot forum is more appropriate?

Last fiddled with by Dubslow on 2015-11-28 at 11:38

2015-11-28, 12:01   #5
davar55

May 2004
New York City

23·232 Posts

Quote:
 Originally Posted by Dubslow Note that the rechenkraft version is currently not quite up to date with some typo fixes, a couple of incorrect statements removed, and of course the lack of the proof axn provided. Use this for now. ... Please. Though perhaps the thread in the aliquot forum is more appropriate?
That is where I still see the missing parentheses.

I just happened on your post here, and so started reading your aliquot paper version, and found this
possible typo. I may look into more later.

2015-11-28, 18:53   #6
davar55

May 2004
New York City

23×232 Posts

Quote:
 Originally Posted by davar55 That is where I still see the missing parentheses. I just happened on your post here, and so started reading your aliquot paper version, and found this possible typo. I may look into more later.
I should have asked you whether you caught the typo already.
The document is yours, of course.

The next typo is in (p-to-the-a minus 1) / (p - 1) [ you wrote b for a ].

I'll stop now. Wish you success.

Last fiddled with by davar55 on 2015-11-28 at 18:57

 2015-11-29, 05:06 #7 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40b typo's been fixed
2015-11-29, 11:43   #8
Happy5214

"Alexander"
Nov 2008
The Alamo City

1101110012 Posts
Introduction to Aliquot Analysis

Quote:
 Originally Posted by Dubslow Happy, your analysis is indeed correct. Though I am curious, how did you come up with the twos count of prime powers? The proof isn't exactly trivial.
Luck? As I said, I'm not a math expert. I'm actually a college student with a CS major. IIRC, I just used Python to calculate a bunch of 2s counts for prime powers and noticed the pattern I described. Thanks for the validation. It was just time and pattern recognition on my part. No rigorous mathematical proofs involved. Not very impressive, but it still worked.

2015-11-29, 12:23   #9
Dubslow
Basketry That Evening!

"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

1C3516 Posts

Quote:
 Originally Posted by Happy5214 Luck? As I said, I'm not a math expert. I'm actually a college student with a CS major. IIRC, I just used Python to calculate a bunch of 2s counts for prime powers and noticed the pattern I described. Thanks for the validation. It was just time and pattern recognition on my part. No rigorous mathematical proofs involved. Not very impressive, but it still worked.
That's actually exactly what I did!

http://htmlpreview.github.io/?http:/...imepowers.html

"But in fact, in my numerical tests, I have been unable to find a counter example where τ(p^a)≠τ(p)+β(l) [where a=2l-1], where the search extended to p<10^9, and each prime was tested up to a=99."

^ said tests were run in Python, and they're what made me look for the proof at all (which axn provided ). In fact, all code I've ever written for aliquot sequences, including the website, is written in Python.

Last fiddled with by Dubslow on 2015-11-29 at 12:24

2015-11-29, 13:54   #10
davar55

May 2004
New York City

23×232 Posts

Quote:
 Originally Posted by Dubslow You still see missing parens? Where? The a->b typo's been fixed
Both fixed.

 2015-11-29, 22:44 #11 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 5·19·61 Posts I am slowly working through your page. It looks very good so far. Thought I would point out another form of guide: Take $2^8*7*73$ for example $\sigma(73)=74=2*37$. This means that $37 | a(2^8*7*73*37*n)$. This process can be repeated to get $2^8*7*73*37*19*5*3*n$ which can't loose 7, 73, 37, 19, 5 or 3 as a factor. These can be fairly vulnerable to getting squared terms and then loosing the guide but they are fairly stable and are highly abundant. Here is a fairly good example: http://factordb.com/sequences.php?se...nge&fr=0&to=30 Can $2^3*3*5*n$ mutate directly to the form $2^3*3^2*5*n$? It rings a bell that there are restrictions on how 2^3*3*5*n can mutate. Forgive me if this is mentioned. I have only properly read up to section 3 and glanced at the rest.

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