Aliquot sequences that start on the integer powers n^i

[EdH]

Originally Posted by EdH

. . .
I will do even more study and post something extra later. . .

I reran the above using only 2⁴ and came up with 70 unbroken and 296 broken. This shouldn't be too far off. Some variations may not be considered, but the runs still appear to break much more often than not.

Perhaps I should look at other drivers/guides?

I can't seem to find the page which describes the difference between drivers and guides. Is it still available somewhere?

[VBCurtis]

Squaring the 31 is the manner in which one breaks 2^4 * 31.
Other powers of 2 would not be a driver; only the perfect number 496 = 2^4 * 31 is a driver.
I believe the same is true for the other perfect numbers: Square the 3 or 7 or 127 to escape.

[LaurV]

Originally Posted by VBCurtis

I believe the same is true for the other perfect numbers: Square the 3 or 7 or 127 to escape.

Yep. There is a thread discussing the math, somewhere here around.

[richs]

Originally Posted by richs

439^40 is now at i554 (added 515 lines) and a C122 level with a 2^2 * 5 * 7 driver, so I will drop this reservation. The remaining C116 term is well ecm'ed and is ready for nfs.

Taking 439^42 at i15 and 439^44 at i2.

439^42 is now at i65 (added 50 lines) and a C131 level with a 2^3 * 3 * 5 driver so I will drop this reservation. The remaining C126 term is well ecm'ed and is ready for GNFS.

Continuing with 439^44.

[garambois]

Page updated.
Many thanks to all for your help !

[unconnected]

I'm done with base 79 - all sequences in the table are >120 digits with >110 ECM-ed composites. Also I did some work with odd k's above the limit, will post results later.

[garambois]

Originally Posted by unconnected

I'm done with base 79 - all sequences in the table are >120 digits with >110 ECM-ed composites.

OK, I will make the next update in one or two weeks.

Originally Posted by unconnected

Also I did some work with odd k's above the limit, will post results later.

All right, keep me posted. I can always extend the base by adding more exponents.


Many thanks !

[RichD]

One of the next logical tables would be 242 (2 * 11^2). I've taken it to i=52.

Edit: Updates to tables 29, 220, 284.

[garambois]

Originally Posted by RichD

One of the next logical tables would be 242 (2 * 11^2). I've taken it to i=52.

Edit: Updates to tables 29, 220, 284.

I will update all the bases on the weekend of December 20th.
And I will also add the base 242 that you calculated.
Thus, the base 200 = 2 * 10^2 will be missing, if you like the bases for which the calculations end for all the exponents. These bases will be interesting for future analyses.

[RichD]

Originally Posted by garambois

Thus, the base 200 = 2 * 10^2 will be missing, if you like the bases for which the calculations end for all the exponents. These bases will be interesting for future analyses.

I'm on it.

[garambois]

OK, many thanks for your help !