Hmm.
why should my model be very rough?
I have trained it with 30 million Factorizations on hard numbers (no factor below n^1/3). For different fixed multipliers m and collection good k = k' * m.
We have only 10.000 = 2^13,33 = 2^(40/3) multipliers 'k' for n below 40 bits. So I think the model is well trained. Increasing the training does not improve the results.
Surprisingly I get best results for the fixed multiplier m = 45.
I do not get the same speed for m=1 or other multiplier below.
So my conclusion is:
It still looks like when factoring one number it is better to go with one fixed multiplier (for us 315), then to go with good multipliers working for other numbers.
Quote:
maximum(S/(m^1/3)) and m < n^1/3,

m < n^1/3 is clear , but i did not get the first limit. And limit on what?
I understand that constructing 'k' as a product of small numbers sounds promising, since it covers many u*v of u/v ~ q/p. But my tries in using this fail. I tired:
 increase multiple different m in parallel
 construct smooth numbers
 use good 'k' from other factorizations.