[seqfan] Re: Is it possible to find a 5-imperfect number for A127724

[Allan Wechsler]

Since these messages came through, I have been happily exploring the world
of imperfect numbers.

Today I found the following order-3 example:

9724440030615707933538533602112206636800 = 2^8 3^7 5^2 7^8 19^2 41 43
117307^2 13760814943

I cannot find it among the resources listed at http://oeis.org/A127724, so
it's possible that this one may have been overlooked by earlier searchers.

I am working on collating the given resources into a couple of text files,
to make it easier to determine if an imperfect number has been seen before.
One file is sorted by size, and the other is sorted "alphabetically" by
prime factorization (so it lists 2 3^2 7 = 126 before 2^2 3 = 12).

I have annotated my files with attributions like [Iannucci 2006], but I
would love to get more detail in my attributions before I make my lists
public. I would especially like to hear from any of the contributors listed
in the links section at A127724, so that I can learn more about the
discovery circumstances of these interesting numbers.

On Fri, Jan 26, 2018 at 6:36 AM, Peter Munn <techsubs at pearceneptune.co.uk>
wrote:

> Please note, for "4.5" below, I intended "4.75".
>
> On Fri, January 26, 2018 2:35 am, Peter Munn wrote:
> > Hi Michel and seqfans,
> >
> > I have plotted (against x/rho(x)) the log(log(x)) of your least known
> > values of x that give specific low-denominator (x/rho(x)). The latest two
> > finds that you report appear on my graph to re-inforce a trend; and I
> note
> > that discovery of a 130- to 180-digit 5-imperfect number would extend
> this
> > apparent trend particularly neatly.
> >
> > The least x with x/rho(x) = 4.5 is a markedly low outlier, so a simple
> > trend is clearly an over-simplification, but I find the trend
> nevertheless
> > tantalising. Plotting values between 3 and 4 would add to the interest, I
> > suspect, as would including the second least values.
> >
> > Best Regards, Peter
> >
> > On Sat, January 20, 2018 6:31 am, michel.marcus at free.fr wrote:
> >>
> >> Dear All,
> >>
> >> I managed to find 2 instances above 19/4 with denominator < 10.
> >>
> >>
> >>
> >> 43/9
> >> 167871214226444261984169560496427984081110737667820375745695
> 6025821219413179225584819784122368000000000000
> >> 29/6
> >> 113215470059694967384672494288288640426795613775971881316864
> 4761600357278655756789762179989504000000000000
> >>
> >>
> >> Michel
> >>
> >> --
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>