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2018-11-21, 20:52   #74
garambois

"Garambois Jean-Luc"
Oct 2011
France

10101011002 Posts

OK, the web page is updated.
Thanks to gd_barnes, richs, kar_bon and LaurV for your calculations and proposals !

Quote:
 Originally Posted by LaurV Hey Jean-Luc, Maybe you can add base 28 too... I added few factorization to the DB for 28^n. I saw you added higher bases, like 439 (?) and I don't know what reason you had, but my opinion is that 28 makes more sense than 439 or 10^x (6^n, 28^n or even 496^n can be seen as powers of perfect numbers, or "powers of drivers", in fact that was what "tickled" my interest for base 6 in the past).

I think that's a good idea !
Besides, it's quite odd that there are only green and blue cells for the moment, but it must be a coincidence !

Some explanations

This web page (aliquot sequences that start on n^i) exists because we have an annoying question on this other web page : http://www.aliquotes.com/existence_s...ini_primes.htm (but sorry in french !).
To try to summarize the question in English :
Can there be an indefinitely growing aliquot sequence in which all terms would be composed of a finite number of prime numbers, but could have any powers ?
We think the answer to that question is "no", but we don't know how to tackle this problem ! However, we would like to get rid of this issue, because we have programs that may be running unnecessarily and are trying to find such aliquot sequences.
The basic idea is therefore to calculate the aliquot sequences that start on integer powers of prime numbers in a first step.
We try very small primes (2, 3, 5...), larger one (439) and a very large one (10^10+19).
We are trying to see if we could "notice" something in the behaviour of these aliquot sequences.
We also do some calculations with slightly composed numbers:
6, 10, 12, 28...
But later, if many people help us with the calculations, we would also like to add the bases with as many prime numbers as possible:
2*3, 2*3*5, 2*3*5*7, 2*3*5*7*11, 2*3*5*7*11*13, .............., and more generally p# with p=53 at least !
Thus, we will observe if the aliquot sequences behave very differently and especially which prime numbers appear in the decomposition of the successive terms of these aliquot sequences.

I hope my explanations are clear !

Last fiddled with by EdH on 2020-06-01 at 12:27 Reason: Link fix and a correction per OP instructions.