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

Peter Munn techsubs at pearceneptune.co.uk
Fri Jan 26 03:35:49 CET 2018


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
> 1678712142264442619841695604964279840811107376678203757456956025821219413179225584819784122368000000000000
> 29/6
> 1132154700596949673846724942882886404267956137759718813168644761600357278655756789762179989504000000000000
>
>
> Michel
>
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