Broken aliquot sequences

[garambois]

I think I found a new aliquot sequence with error on FactorDB. It's a sequence that starts with a number < 3,000,000 which is on the blue page.


This is the sequence that starts with 1475172, error at index 255.

Can anyone confirm ?

253 .   152340387197383120612 = 2^2 * 113 * 337036254861467081
254 .   116614544182067610824 = 2^3 * 17 * 2371 * 4211 * 140297 * 612137
255 .   115052270138377872376 = 2^3 * 457 * 80233 * 278219 * 1409773
256 .   101146402985461010024 = 2^3 * 3727 * 3392353199136739
257 .   88553987910265490776 = 2^3 * 11069248488783186347

should be :

253 : 152340387197383120612 = 2^2 * 113 * 337036254861467081
254 : 116614544182067610824 = 2^3 * 17 * 2371 * 4211 * 140297 * 612137
255 : 115054299854133875896 = 2^3 * 14381787481766734487
256 : 100672512372367141424 = 2^4 * 2503 * 2513796253804613
257 : 94458408032962215712 = 2^5 * 442571 * 6669721357771

[Happy5214]

Both the Python mfaliquot library and WolframAlpha support the second version, so it appears the sequence is indeed broken in FactorDB.

[garambois]

I probably found yet another mistake :

A new aliquot sequence with error on FactorDB.
It's a sequence that starts with a number < 3,000,000 which is on the blue page.


This is the sequence that starts with 1866192, error at index 3835.

Can anyone confirm ?

3833 .   1857136161022787663609287672 = 2^3 * 19 * 53 * 1072637 * 214917368946554501
3834 .   1877426135009140448634383528 = 2^3 * 947 * 977 * 394747 * 2138897 * 300413621
3835 .   1650071913384946652798107672 = 2^3 * 19 * 6163 * 49009 * 35941092589041083
3836 .   1607243861666293749034420328 = 2^3 * 11 * 18264134791662428966300231
3837 .   1680300400832943464899621432 = 2^3 * 71 * 2958275353579125818485249

should be :

3833 : 1857136161022787663609287672 = 2^3 * 19 * 53 * 1072637 * 214917368946554501
3834 : 1877426135009140448634383528 = 2^3 * 947 * 977 * 394747 * 2138897 * 300413621
3835 : 1650082498696992926527054552 = 2^3 * 631 * 1109 * 65089 * 33131089 * 136682041
3836 : 1451567367500391297153505448 = 2^3 * 137 * 24708664649 * 53601552304837
3837 : 1289987788382339502020263552 = 2^7 * 7 * 405382183 * 3551509104729389

[EdH]

Confirmed! This is what Aliqueit tells me:

Verifying index 3835... 
ERROR: @index 3835: value != sigma - n

Corrected lines match yours:

 3835 .     1650082498696992926527054552 = 2^3 * 631 * 1109 * 65089 * 33131089 * 136682041
 3836 .     1451567367500391297153505448 = 2^3 * 137 * 24708664649 * 53601552304837
 3837 .     1289987788382339502020263552 = 2^7 * 7 * 405382183 * 3551509104729389
 3838 .     1647037987054673586242766848 = 2^11 * 7 * 321403 * 52293193 * 6835661317

[garambois]

OK, verification of all aliquot sequences starting with numbers less than 3,000,000 is complete.
Thanks to Happy5214 and EdH for confirming errors found on factorDB.

Can someone please give me the last 80-digit terms of the 3 broken aliquot sequences on FactorDB ?

933564
1475172
1866192

I need these 3 terms to complete my updated C80 database I was talking about here :
https://www.mersenneforum.org/showthread.php?t=24423

I hope someone has those three 80 digits terms...
If not, I will have to delete these three aliquot sequences from my C80 database.


Excuse me, but may I also point out that the two errors reported recently were not reported on the blue page.

[EdH]

I think these are the correct last c80's for the unbroken three sequences:

933564 = 53910798253283852177545053052282940198337166755985147396297057839253859396629560
1475172 = 70632199920744621702989746940578378226575559519111823940659865966774451778707304
1866192 = 97488918894772105620549720764059516378747055783492651624463822352092076013025324

These are not from the broken elf's, but from what should have been the correct elf's later on.

[garambois]

Thank you very much EdH !
This is exactly what I needed.



How did you get the data for these three aliquot sequences ?


I realize that an aliquot sequence merge is detected when entering data into the FactorDB database.
Any merge detected using one of the three broken aliquot sequence on FactorDB will be false...

[EdH]

Originally Posted by garambois

Thank you very much EdH !
This is exactly what I needed.



How did you get the data for these three aliquot sequences ?


I realize that an aliquot sequence merge is detected when entering data into the FactorDB database.
Any merge detected using one of the three broken aliquot sequence on FactorDB will be false...

Here are the steps I took for 933564 (which included writing a couple scripts to fix the numbering and search for the last c80):

1. - download 933564.elf
2. - rename to alq_933564.elf
3. - check 933564 with "./aliqueit 933564 -t"
4. - delete the lines after the last valid line
5. - run "./aliqueit 933564 -q"
6. - take last composite from alq_933564 (1150187197239087798)
7. - query factordb for sequence 1150187197239087798
8. - download its elf
9. - remove new last line from alq_933564.elf to prevent duplication
10. - splice* the 933564 and 1150187197239087798 elf's together
11. - replace the original alq_933564.elf with the new spliced file
12. - verify the new alq_933564.elf with "./aliqueit 933564 -t"
13. - grab the last c80 in alq_933564.elf

*I wrote a script to renumber the new spliced file as it joined them, because simply concatenating would leave the original indices for the second elf.

splice-elf.sh script:

#!/bin/bash

count=0
exec <"$1"
  while read line
    do
      period=$(echo `expr index "$line" .`)
      echo "${count} ${line:$period-1}" >>new.elf
      let count=${count}+1
    done
 
exec <"$2"
  while read line
    do
      period=$(echo `expr index "$line" .`)
      echo "${count} ${line:$period-1}" >>new.elf
      let count=${count}+1
    done

[garambois]

Thank you very much EdH for this method, I hadn't thought of it !
I can reproduce it with my own means...

[EdH]

You're quite welcome. Glad I was able to help.

[LaurV]

Originally Posted by EdH

*I wrote a script to renumber the new spliced file as it joined them, because simply concatenating would leave the original indices for the second elf.

Nice job. Used to do all this procedure with the editor, in both pn2 and notepad++ you can mark/delete rectangular blocks (using shift+alt) and auto-number text lines. It is only a couple of cut/paste and takes a minute.