I think there are a few misunderstandings around this particular tree as the figures do not appear to be correct
What we are aiming at here is to maximise the image data we have and not leave any IQ on the table. It is quite possible that you could print at any old ppi and still get acceptable results but you would be working in less than optimal conditions and just may leave a little IQ behind as a result.
Your printer can lay down a maximum of 9600 droplets per inch in one direction (horizontal) and 2400 droplets per inch in the other (vertical) this is achieved by the feed mechanism being inched fractionally between passes of the print head.
A pro. Canon print head has 300 nozzles in the print head and this is the standard resolution it reports to your computer OS. It also has a fine mode that is reported as 600 ppi, achieved by micro stepping between passes. Epson are based on 360/720 ppi. It is also possible that they could have 150 or 180 nozzles respectively
A4 is actually 210 × 297 millimeters or 8.27 × 11.69 inches, but we can largely ignore that for the moment and concentrate on your image files native pixel count (the print diagonal does not really matter for this purpose)
Pentax K1 7360×4912 pixels when sent to the printer at
300 ppi will give a print size of 24.53" x 16.37" (rounded)
Pentax K1 7360×4912 pixels when sent to the printer at
600 ppi will give a print size of 12.26" x 8.19" (rounded)
It is quite easy in LR to see what figures your are sending as in the examples in this thread.
Maybe it will help to remember that:
If at your required print size the ppi is anything below 300 you should set LR to upsample to 300 ppi
or
If at your required print size the ppi is above 300 you should set LR to upsample to 600 ppi.
It is less than optimal to set values in between such as 400 etc and is better practice to send the data as declared to the OS and let LR or PS handle the sampling rather than the print driver. So if you do end up with a 400 ppi figure then set LR to 600 ppi.
In trying to make it easy I hope I have not complicated it
.