Here's how it works.
We start with a pile of integers, from 1 to
some number that you choose. You take one, and I get all the others
that divide it evenly. We repeat until there's nothing left.
BUT (big but!) I have to get something on each turn. So when
none of the numbers in the list have any divisors that have not been taken,
I take them all.
Your score is the sum of all the numbers you took, while my
score is the sum of all the numbers I took.

Numbers that you can pick are green.
Numbers that you have taken are bright yellow
when first picked, later dark yellow.
Numbers that I have taken are red
at first, then later, pink.
Numbers that you can't take because they have no divisors left
are gray.
(I get all of those eventually!)
At the end of the game, the leftover numbers that are mine are
dark pink.