mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Aliquot Sequences

Reply
 
Thread Tools
Old 2017-02-21, 10:29   #12
AndrewWalker
 
AndrewWalker's Avatar
 
Mar 2015
Australia

1228 Posts
Default

Quote:
Originally Posted by garambois View Post
Does anyone know if there is an instruction in Sage software that can compute sigma (z), where z is an integer complex number of Gauss : the equivalent of the DivisorSigma[1, z, GaussianInteger-> True] function of Mathematica and sigma being the sum of the divisors extended to complex numbers according to Spira's proposition in 1961? See here for a better understanding of my question :

https://oeis.org/A102506

or

http://mathworld.wolfram.com/DivisorFunction.html
When I was doing the searching I posted about earlier, I searched through some of the sage packages such as mpmath and couldn't find anything else to caculate sigma for gaussian integers. You can call pari routines in sage, or just use the regular pari program and my routine I posted earlier.

I've only explored sigma(z)-z, so I don't know if iterating sigma(z) is interesting or not.
AndrewWalker is offline   Reply With Quote
Old 2017-02-23, 11:12   #13
garambois
 
garambois's Avatar
 
Oct 2011

3·5·17 Posts
Default

Thank you for your help Andrew.

garambois is online now   Reply With Quote
Old 2017-05-08, 07:49   #14
AndrewWalker
 
AndrewWalker's Avatar
 
Mar 2015
Australia

2×41 Posts
Default

I've been doing a bit more searching this year, here is my latest list which has 304 gaussian amicable pairs. It's getting harder to find them now!
Attached Files
File Type: txt GaussListMaster2.txt (11.7 KB, 103 views)
AndrewWalker is offline   Reply With Quote
Old 2017-08-28, 09:11   #15
AndrewWalker
 
AndrewWalker's Avatar
 
Mar 2015
Australia

2·41 Posts
Default

A big update, now have 423 pairs! Many of these come from searching a common factor
with 4 extra small factors which I had done very little with earlier. Plus also many from
3 extra small factors

Andrew
Attached Files
File Type: txt GaussListMaster3.txt (16.7 KB, 57 views)
AndrewWalker is offline   Reply With Quote
Old 2017-12-14, 10:05   #16
AndrewWalker
 
AndrewWalker's Avatar
 
Mar 2015
Australia

2·41 Posts
Default

More of the same searching, now 515 pairs

Andrew
Attached Files
File Type: txt GaussListMaster4.txt (20.6 KB, 59 views)
AndrewWalker is offline   Reply With Quote
Old 2018-01-11, 11:57   #17
AndrewWalker
 
AndrewWalker's Avatar
 
Mar 2015
Australia

2×41 Posts
Default

I discovered that pari when writing a factorisation to a file leaves it on one line! So with
a bit of extra find/replace manipulation in Word here is a list of the pairs with factorisations.

There still could be a number of errors in this so if you spot any thing odd or just plain wrong please let me know!
Attached Files
File Type: txt GaussListMaster4Fac.txt (80.2 KB, 60 views)
AndrewWalker is offline   Reply With Quote
Old 2018-06-17, 07:58   #18
AndrewWalker
 
AndrewWalker's Avatar
 
Mar 2015
Australia

10100102 Posts
Default

Next update at 600 pairs, very close!
AndrewWalker is offline   Reply With Quote
Old 2018-06-24, 08:27   #19
AndrewWalker
 
AndrewWalker's Avatar
 
Mar 2015
Australia

2·41 Posts
Default

Pair 600 found today


Again please let me know if you spot any errors.


Andrew
Attached Files
File Type: txt GaussListMaster5Fac.txt (94.5 KB, 47 views)
AndrewWalker is offline   Reply With Quote
Old 2018-11-30, 08:18   #20
AndrewWalker
 
AndrewWalker's Avatar
 
Mar 2015
Australia

2×41 Posts
Default

Looks like I've probably reached 750 pairs, will do a stocktake and add some comments over the weekend!


Andrew
AndrewWalker is offline   Reply With Quote
Old 2018-12-04, 06:33   #21
AndrewWalker
 
AndrewWalker's Avatar
 
Mar 2015
Australia

2·41 Posts
Default

760 pairs!


I've found quite a few in the last few weeks, including some new largest pairs,
as I had the idea to search on (1+I)^m * (1+2I)^n * (1+4I) (multiplied by extra prime factors) which I'd never done before, had only used two of these factors at a time.
I've found pairs using this with m up to 15 and n up to 4.
I haven't found any pairs of any form with (1+4I) being a power of 2 or more.


Andrew
Attached Files
File Type: txt GaussListMaster6.txt (31.4 KB, 32 views)
AndrewWalker is offline   Reply With Quote
Old 2019-08-09, 10:07   #22
garambois
 
garambois's Avatar
 
Oct 2011

3·5·17 Posts
Default

Has anyone ever tried to find complex social chains of any length other than 2 (other than complex amicable numbers presented by Andrew Walker just above) ?
garambois is online now   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
pari-algorithm for finding Gaussian integer bases devarajkandadai Software 0 2017-10-05 04:54
pari-algorithm for finding Gaussian integer bases devarajkandadai Software 0 2017-07-11 05:42
Broken aliquot sequences schickel FactorDB 18 2013-06-12 16:09
poaching aliquot sequences... Andi47 FactorDB 21 2011-12-29 21:11
New article on aliquot sequences schickel mersennewiki 0 2008-12-30 07:07

All times are UTC. The time now is 13:31.

Fri Jul 10 13:31:10 UTC 2020 up 107 days, 11:04, 2 users, load averages: 1.85, 1.71, 1.57

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.