"These printers, such as the models 870/1270/2000P are (somewhat misleadingly) listed as 1440 dpi printers. This means that they are capable of laying down that many dots per inch. But, to create a color image they need to use 6 different inks, so any particular pixel reproduced on a print will be composed of some dithered composite of colored dots using some or all of these inks. That’s why you need more dots from your printer than you have pixels in your image.
If you divide 1440 by 6 you end up with 240. This is the true minimum resolution needed to get a high-quality photo-realistic print from a 1440 dpi Epson printer. Many users, myself included, believe that a 360 ppi output file can produce a somewhat better print. If my original scan is big enough to allow this I’ll do so but I don’t bother ressing up a file to more than 240 ppi when making large prints."
I don't understand why you'd divide the marking engine pitch by the number of inks to get the resolution you need in the file fed to the halftoning software. It seems totally nonsensical.
The Epson halftoning software in the driver has, as far as I know, always resampled the input image to 360 ppi.
Jim