[seqfan] Re: Median nth least factors in prime factorisations of the integers
Neil Sloane
njasloane at gmail.com
Sat Apr 1 19:16:29 CEST 2017
Peter, You should be aware than in mathematics, when one says that
"most" things have a certain property, it means "all except a finite
number".
In your submissions A284411 and A281889 you used "most" to mean
"strictly more than half". This is too different from the standard
usage, so I have
changed the definitions to make it clear what you meant.
You can't redefine a standard terminology to be anything you want!
Best regards
Neil
Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
On Fri, Mar 31, 2017 at 2:38 PM, Peter Munn
<techsubs at pearceneptune.co.uk> wrote:
> Dear Seq Fans,
>
> This concerns my first significant piece of mathematical work since my BSc
> 40 years ago! Note I suggest checking of A281889(4).
>
> Best Regards,
> Peter Munn
>
> Background
> ==========
>
> I've been looking at prime factorisations with factors listed least first
> and examining how "quickly" the values "typically" grow from factor to
> factor. (More detail on https://oeis.org/wiki/User:Peter_Munn)
>
> I have now proposed sequences of medians for both n-th least prime factor
> value in prime power factorisations (A284411) and n-th least listed factor
> in the simpler prime factorisation with a straight product of prime
> numbers (A281889), but with definitions that emphasise their distinctness.
>
> In the first case, my calculation of terms 2 and 3 led via Google to the
> 4th term in the form of an advert for De Koninck's _Those Fascinating
> Numbers_. So I'm happy with A284411. But I have yet to find the terms of
> A281889 (3, 7, 433, 9257821) elsewhere, and so...
>
> My calculation check suggestion
> ===============================
>
> I have checked my calculation method against empirical counts, and looked
> at rounding errors, but I see scope for an error in complexity I added in
> order to calculate A281889(4) on a limited platform. So I would
> appreciate an independent calculation, whether or not based on the
> formulae I give in A281890 and A281891 which underpin the sequence.
>
> Many thanks if you can help,
>
> Peter
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