(50g) Möbius function (MOB)

[Joe Horn]

(03-16-2018 07:25 PM)DavidM Wrote:  

(03-16-2018 02:34 PM)Joe Horn Wrote:  The Möbius function, used in number theory, usually written as μ(n) but called MOB(n) here, is defined thus...

I'm afraid the wikipedia function description leaves my head spinning as to what you might intend to do with this now that you have it. Are you using it for something special? Or would that description leave my head spinning the opposite direction?

Short answer: I use it mostly when playing around with multiplicative functions, as explained here: https://brilliant.org/wiki/mobius-functi...s-function
Here's an interesting blog posting about it: https://rjlipton.wordpress.com/2011/02/2...-function/

Long answer: When playing with numbers, I always write tiny RPL routines to perform snippets of the task at hand. These are used at the time but soon abandoned and forgotten about. Such routines accumulate in RAM, and I hate to purge them because I know they were useful once upon a time, but I no longer remember what they are for. For example, the following routine is currently in my 50g, called 'PR.2' (on page 50 of my HOME directory):

\<< NPR \GSLIST OVER MODSTO EXPANDMOD OVER EULER MOB \>>

It calls MOB... but I have NO IDEA what it was intended for, nor what its name meant. Its first command is NPR, which is a global label, which no longer exists in my 50g! Many such ghosts haunt my 50g's RAM.

I also have a few other routines that call MOB, as well as routines that call THOSE routines, and so on... but I don't remember what any of them are for. They are playthings which were abandoned and forgotten as new playthings were discovered. Just goes to show that HP 50g memory is more tenacious than my own brain's memory. I suspect that many MoHPC members have similar experiences.