When using the verb "to note" in the sense of "to write down", for example,
Note that down so you will remember it
is the down necessary or not? Does
Note that so you will remember it
also have the meaning of writing something down (aside from the other meaning of "to note")? To me, the second variant seems to be a false friend often used by German speakers, because in German the corresponding expression is "sich etwas notieren".
The reason why I am not sure is that the OALD mentions the phrasal verb "to note something down", but Merriam-Webster also includes "to say or write something" as a possible meaning of "to note".