[seqfan] Median nth least factors in prime factorisations of the integers

Peter Munn techsubs at pearceneptune.co.uk
Fri Mar 31 20:38:41 CEST 2017

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


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,


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