Two games on arithmetic functions: SALIQUANT and NONTOTIENT
Paul Ellis, Jason Shi, Thotsaporn Aek Thanatipanonda, Andrew Tu · Discrete Mathematics Letters · 2023
We investigate the Sprague-Grundy sequences for two normal-play impartial games based on arithmetic functions, first described by Iannucci and Larsson in a book chapter.In each game, the set of positions is N.In saliquant, the options are to subtract a non-divisor.Here we obtain several nice number theoretic lemmas, a fundamental theorem, and two conjectures about the eventual density of Sprague-Grundy values.In nontotient, the only option is to subtract the number of relatively prime residues.Here we are able to calculate certain Sprague-Grundy values and start to understand an appropriate class function.