20090710, 17:22  #1 
Nov 2008
2·3^{3}·43 Posts 
Getting started
Welcome to the weird and wonderful world of Aliquot Sequences! This is an exciting project, because it is a mix of most factorization methods, when you have finished one number you get a new one, and (AFAIK) it is the only factorization project that can make your pulse rate increase by 50% (albeit only for a couple of minutes).
Aliquot sequences are formed by taking one number, adding up all its factors except the number itself, and repeating the process on the new number. So, if you start with 12, you work out 1+2+3+4+6, which comes to 16. Repeat and you get 15, 9, 4, 3, 1. When a sequence reaches 1 it terminates. It also terminates if it ends up in a perfect number or aliquot cycle. Sequences are generally referred to by their starting value. You can read more about aliquot sequences on some of the pages in the useful links thread. The smallest factors of a term in an aliquot sequence make up the driver or guide, and these determine whether the sequence will go down (good) or up (bad). You can read about them here. This project has three parts. The first part is the "main" project. We are working on sequences with starting values below 1000000, focusing on stable sequences that may acquire the downdriver (if you have read the above links (you should have done), you will know what those are). This part of the project is best if you want to break records for things like highest downdriver acquisition. Look in the ranges and status and reservations threads for information on which sequences are reservable. The second part of the project is (are?) the subprojects and special projects. These are the aliquot sequence version of RPS and NPLB "drives". In the subprojects, we take a large range to a specific height or try to escape drivers. The third part of the project is where we collaborate and work on one sequence, right now 4788 which is over 160 digits. This results in large team GNFS jobs. This is the best section if you don't want to work on a sequence of your own. Now for the exciting bits: how to contribute! Download aliqueit from here. There are Windows executables and source code included. Also download GMPECM, Msieve, Yafu and GGNFS from the "External factoring Programs" links. Put GMPECM, Msieve and Yafu in your aliqueit folder. Modify the paths in aliqueit.ini so they correspond with the paths of your binaries (note: yafu path must be kept as just "yafu", it seems to crash if you use the full path). "gnfs_cutoff" defines the cutoff between running Yafu and GGNFS, and the optimum value (the point at which GGNFS becomes faster than Yafu) depends on your system. 100 is a good starting value, but it is lower for 64bit Linux due to faster sievers. Create a folder for GGNFS. Now make all the adjustments to msieve (i.e. versions), factMsieve.pl etc. mentioned here. You will need perl installed (latest version recommended). Modify the paths in aliqueit.ini so they point to your perl executable and factMsieve.pl. NOTE: factmsieve.py is not fully bugfree yet, so please use the .pl script. If you want to participate in a subproject, have a look in one of the subproject threads, reserve the sequence in a post in that thread, and release it in another post when it reaches the subproject target size. If you want to run a sequence for the "main" project, find a sequence that you want to reserve, and reserve it in the reservations thread. Once you have chosen your sequence, go onto factorDB, click on "Sequences" (at the top), enter the sequence number and click "Show". Then click on "Download .elf file" (just below "Show"). Save the file in your aliqueit folder and rename it from <the sequence>.elf to alq_<the sequence>.elf, where <the sequence> is the initial term of the sequence. Now, run "aliqueit <the sequence>" from cmd/shell/whatever it is for your OS. Aliqueit will start! 100digit composites should take a couple of hours to GNFS on a recent processor, 120digit composites will take a couple of days. The time it takes for a sequence to reach a certain height is nowhere near certain  downdriver runs may mean that it takes ages. If you interrupt aliqueit while msieve, yafu or GGNFS is running, just restart with "aliqueit <the sequence> e". If you want to run everything at low priority, run "aliqueit <the sequence> p". Alternatively, Yafu can run the ECM and GNFS steps if the y switch is added. To prepare for this, remove all the "tune_info" lines from yafu.ini (Yafu's config file), and then run "yafu tune()". This computes the GNFS cutoff for your machine, and adds a new "tune_info" line to yafu.ini. Note that this overrides the "gnfs_cutoff" in aliqueit.ini. Using Yafu for ECM and GGNFS requires the paths to the GGNFS folder and ECM binary to be set in yafu.ini. This method allows efficient multithreading of one sequence  change the "threads" parameter in yafu.ini. However, restarting after interruptions is not as easy, especially as there is an unresolved bug in this process. To submit all your work on a sequence to factorDB, run "aliqueit <the sequence> s 0". Always do this when you release a sequence. To release sequences, just post in the reservations thread. Have fun! P.S. Post here or send me or one of the other mods a PM if you feel I've left something out or if you have other questions about the project. Last fiddled with by schickel on 20120324 at 01:35 Reason: Update analysis page to point at Internet Archive 
20090710, 18:11  #2 
Sep 2004
2×5×283 Posts 
worker.exe is the automated client for Aliquot Sequences?

20090710, 18:23  #3 
Mar 2007
Germany
2^{3}·3·11 Posts 
No the worker.exe does all incoming work on Syds Database  not only aliquot sequences. The aliqueit.exe is doing only aliquot sequences.

20090710, 18:35  #4 
A Sunny Moo
Aug 2007
USA (GMT5)
14151_{8} Posts 

20090710, 18:36  #5 
Nov 2008
2×3^{3}×43 Posts 
Worker.exe will sometimes get a number from an aliquot sequence, but it gets loads of others too.
Last fiddled with by 10metreh on 20090710 at 19:24 Reason: Removed accidental offence 
20090720, 18:37  #6  
Sep 2004
2×5×283 Posts 
Quote:
10metreh: AFAIK that isn't supported yet. The database thread (in the main Factoring forum) is the place to ask for that to be supported. However, Syd seems to be taking a summer break. Last fiddled with by 10metreh on 20090720 at 18:48 

20090723, 16:45  #7 
(loop (#_fork))
Feb 2006
Cambridge, England
2·13^{2}·19 Posts 
Dumb driver question
I have an exceedingly stupid question.
For numbers 496k, k=10^10 .. 10^10+10^5, 55% have the sum of divisors not divisible by 496; and about the same proportion for 10^20 .. 10^20+10^5. But once I have a number divisible by 2^4*31 in an aliquot sequence (246558), getting rid of the 31 seems very hard; I can turn it into 31^2 occasionally, but it always seems to go back to 31 at the next cycle (ah. If I restrict to numbers which are divisible by 2^4*31 and not by 2^5 or 31^2, it always goes back to 2^4*31; if I have a factor 31^2 then there seems to be an about 0.4 chance of losing the 31 next time, I've just been unlucky twice. But the stake for this 5:2 bet is about 31 large factorisations ...) Last fiddled with by fivemack on 20090723 at 16:57 
20090723, 16:58  #8  
Nov 2008
100100010010_{2} Posts 
Quote:
Ah, seen the edit... Last fiddled with by 10metreh on 20090723 at 17:22 

20100525, 14:36  #9 
Apr 2010
Over the rainbow
2^{3}·5^{2}·13 Posts 
ok, i have some problem understanding how it does work...
for example, 128370 the 'first' factor are 2*3*5*11*389, wich is 128370, indeed. but from what i have read, the next step would be 2+3+5+11+389+128370=128908 128908128370=589 (why bother adding the first number?) and it appear that the second 'seed' is 208590... how come? nvm.. i understood... should have added 6,10,22,778,15,33,1167,4279,30,55,2334,88,3112,6224,330 ,11670 and various other multiplication i forgot Last fiddled with by firejuggler on 20100525 at 15:34 
20100525, 17:25  #10 
Nov 2008
2·3^{3}·43 Posts 
Because when aliquot sequences are actually calculated, it is actually the sum of all the factors that is calculated first (because there is a formula for it), and the number itself is subtracted. But if you're looking at the actual definition, yes, there is no point in adding the number and then subtracting it. Edited the post. I've also changed the example from 10 to 12 to make it clear that all factors, not just prime factors, are added together.
Also, there is only one subproject currently running, not two as the post claimed until about 30 seconds ago. Last fiddled with by 10metreh on 20100525 at 17:29 
20120323, 21:46  #11 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
Alright, I'm trying not to bug anybody and read the alreadyposted questions, but the link above that's supposed to talk about drivers and guides etc. is down, and the wiki, while like Wikipedia is good for explaining if you already know it, it isn't much use to me. (Why would 6 being a factor of a term mean that the next term will be higher?) It appears that the lafn.org links in general are all down, however the domain's homepage works fine.
Last fiddled with by Dubslow on 20120323 at 21:50 
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