Aliquot sequences that start on the integer powers n^i

[Happy5214]

Originally Posted by Happy5214

... plus 26^67, which had additional terms already in FactorDB that I didn't compute, but I couldn't deduce a merge for. ...

One quick note from base 22, which will finish initializing either later Tuesday or Wednesday, is that 22^67 was also already done to 111 digits. I looked back, and 24^67 was also advanced to a similar depth before I got there, so someone must have made a concerted effort on those i=67 sequences.

[garambois]

Originally Posted by Happy5214

One quick note from base 22, which will finish initializing either later Tuesday or Wednesday, is that 22^67 was also already done to 111 digits. I looked back, and 24^67 was also advanced to a similar depth before I got there, so someone must have made a concerted effort on those i=67 sequences.

This is indeed very curious !
It would seem that for bases 33, 34, 35 and 37 too, calculations were done further for exponent 67.

[yoyo]

I'll take base 26 and 29.

[RichD]

Do we have another merge with 37^30 ?

[Happy5214]

Base 22 has been initialized. There were three merges (22^5:i19=86388:i4, 22^29:i321=5208:i6, and 22^41:i1065=14676:i15). Exponents 1, 3, 7, 11, 19, 21, and 23 terminate, with 22^3 terminating with a perfect number (6).

In unrelated news, I poached several yafu@home sequences with downdrivers (apologies) and terminated 20^71 and 21^70.

[garambois]

Originally Posted by yoyo

I'll take base 26 and 29.

Many thanks !
Next weekend I will do the next update and it will be noted in the tables.

[garambois]

Originally Posted by RichD

Do we have another merge with 37^30 ?

I find the following fusion :
37^30:i1193 with 35856:i3
Many thanks.

[garambois]

Originally Posted by Happy5214

Base 22 has been initialized. There were three merges (22^5:i19=86388:i4, 22^29:i321=5208:i6, and 22^41:i1065=14676:i15). Exponents 1, 3, 7, 11, 19, 21, and 23 terminate, with 22^3 terminating with a perfect number (6).

In unrelated news, I poached several yafu@home sequences with downdrivers (apologies) and terminated 20^71 and 21^70.

Many thanks.
I confirm the accuracy of the mergers.
And so we have one more cycle, which is C1 = 6.
Base 22 will be added in the next update.

Yafu is an extremely powerful tool precisely to allow us to locate the sequences that must be calculated further. Without yafu, it would take months, if not years, to spot these sequences.
We cannot thank yoyo enough for his entry into the project !

[yoyo]

I would take more, but only complete bases.
Which ones are important?
For the while beeing I'll take also base 31 and 33, they seems to be completly unreserved.

[garambois]

Originally Posted by yoyo

I would take more, but only complete bases.
Which ones are important?
For the while beeing I'll take also base 31 and 33, they seems to be completly unreserved.

You mean bases 30 and 31 (and not 31 and 33), because base 33 has not yet started ?

And if you want to take even more, would it be possible to take in priority the perfect number 8128 and the two amicable numbers 220 and 284 ?

Note : In 2 weeks, I will be on vacation and I will take a closer look at the sequences that end with cycles. It is likely that we will have to add additional exponents for the perfect numbers 28, 496 and 8128, we will see...

[yoyo]

Oh, I took 33.
But I'll take 30, 8128, 220, 284 also.