  We investigate the Sprague-Grundy sequences for two normal-play impartial
games based on arithmetic functions, first described by Iannucci and Larsson in
\cite{sum}. In each game, the set of positions is N (natural numbers). 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 are able to calculate certain Sprague-Grundy values, and start
to understand an appropriate class function.
