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

[Peter Munn]

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