20120104, 08:14  #56 
Jul 2009
Aachen, Germany
41 Posts 
In 1988 I wrote a small programme for pocket calculator for a backwardcalculation of an aliquot sequence. It was transformed in UBASIC and runs well. I published some ideas from Jack Alanan in my book "Primzahlfamilien", too.
I zipped the total packet: http://www.aliquot.de/archiv/retour.zip The progamme will run in a DOSWindow. You can study the code of retour.ub and ingold.ub for transforming it on modern PCs. All the best for 2012 and many following years Wolfgang 
20120104, 09:43  #57 
Jul 2009
Aachen, Germany
101001_{2} Posts 
0 : 104
1 : 104 ist der Inhalt von 10609 2 : 104 ist der Inhalt von 202 Der Grad der ZAHL 104 ist : g(104) >= 2 Mit mehrfaktorigen Zerlegungen ist der Grad der ZAHL 104 jetzt: g(104) >= 2 0 : 102 1 : 102 ist der Inhalt von 10201 Der Grad der ZAHL 102 ist : g(102) >= 1 Mit mehrfaktorigen Zerlegungen ist der Grad der ZAHL 102 jetzt: g(102) >= 1 0 : 96 0 : 96 ist vermutlich unberührt Die ZAHL 96 ist vermutlich unberührt, ihr Grad ist 0 Mit mehrfaktorigen Zerlegungen ist der Grad der ZAHL 96 jetzt: g(96) >= 0 
20120105, 03:10  #58 
Mar 2006
Germany
2·3·5^{2}·19 Posts 
Changed version
I've used a different algorithm to calculate and print the sequences.
 no double edges or missing (for example n=104 ending in 41p)  all perfect/amicable displayed correct (like 496 or 1182/1210)  "Open Sequences" printed when greater as a given maximum (mostly on righthand side)  'lonely' values like '5' not printed  the code is much smaller (~ 90 with comments against ~200 lines) Inlcuded is the graphfile for dotty for the range up to n=2000 and the luasource. I've tested also n=10000 but dotty needs some time to display and will not show the whole range of sequences (dottydispaly to small for all). I've not yet displayed special shapes like to original version. Please test/play with and tell errors. Last fiddled with by kar_bon on 20120105 at 03:21 
20120105, 06:12  #59 
Apr 2010
Over the rainbow
2·1,217 Posts 
Writing sequence with only one ">" really helped.
It was stupid to think about writing the entire sequence in one go. to get the odd in plaintext and the circle shape for "perfect" change the second loop to Code:
for i=3, range do  for the given range try to make the sequences while sigma[i] ~= nil and nsigma[i] ~= nil do  avoid to display lonely values, which were never reached if sigma[i] > 100000 then  maximum reached > display as "Open Sequence" io.write(i.."[label=\"OpenSeq\",shape=plaintext];\n") nsigma[i] = nil break end if sigma[i] == 1 then  values reached is prime > mark as "Prime" io.write(i.."[label=\""..i.."p\",shape=plaintext];\n") else io.write(i..">"..sigma[i].."\n")  else normal value if i==sigma[i] then io.write(i.."[shape=circle];\n") end end nsigma[i] = nil  mark edge as already printed (no doubles) i = sigma[i] if i%2==1 then io.write(i.."[shape=plaintext];\n") end end end boxes should happen what at least 2 arrow point to a number and triangle should (that will probably hard and need a third loop) happen when the lowest even number leading to that merge Code:
102>114 114>126 126>186 174>186 186[shape=box]; 102[shape=triangle]; 
20120106, 20:19  #60  
Mar 2006
Germany
2·3·5^{2}·19 Posts 
Quote:
 detect merges and ouput those nodes as box  also perfect numbers and amicable pairs are solved: shown as circle Included the updated source and the graphfile up to n=2000. The harder part with lowest value for a merge is still missing yet. 

20120115, 04:46  #61 
Mar 2006
Germany
2×3×5^{2}×19 Posts 
I've done a first version of a LUAprogram to build a graph backwards from a given sequence with all merges lesser than 1000000.
First I've build a file with all sigmavalues for n<=1000000 (4 bytes for each sequencevalue, so maximum is 4294967295; highest sigma is 3392928 for seq=997920; the file can be extended easily), so the sigmas only have to be calculated once. For a given seq this file is loaded and the tree is build recursively. So far the main sequence is filled with lightblue and the index of the value is given. No shapes yet considered (for example: box for odd values). A GIFimage for the 276tree can be found here (730 kB) (got problems to view in IE, but FF worked). The graphsource file for Graphviz is attached. Please check first before code is given. 
20120115, 15:33  #62 
"Ed Hall"
Dec 2009
Adirondack Mtns
3,373 Posts 
Wow! This is fantastic. I had no idea so many numbers merged into others... So, if/when 276 terminates, all these others will, too.
This image is a great eye opener for me. Thanks for the effort you put in. 
20120115, 16:08  #63 
Sep 2009
2^{3}·239 Posts 
Is anyone working on 276? The c162 is doable given time.
Chris K 
20120115, 16:33  #64  
"Frank <^>"
Dec 2004
CDP Janesville
2·1,049 Posts 
Quote:
However, until the 2 * 3 driver is lost, it is essentially hopeless. (966 was doing pretty badly, too, but I see it has escaped 2^3 * 3; now it just needs to lose the '3'.) 

20120115, 16:42  #65 
Mar 2006
Germany
101100100010_{2} Posts 
Here's the graph for seq 4788 (this time a PNG; 14523 x 3087 pixel; 1,5 MB).
There're 1022 seqs (incl. 4788) < 1000000 in this family. The 'real' 4788tree is rightmost only a little bonsai, but with a big branch of about 1000 seqs! Last fiddled with by kar_bon on 20120115 at 16:43 Reason: 1M 
20120115, 16:55  #66  
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 
Quote:


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