Divisor Nim

Anton and Bertrand love to play three pile Nim. However, after a lot of games of Nim they got bored and changed the rules somewhat. They may only take a number of stones from a pile that is a proper divisor of the number of stones present in the pile. E.g. if a pile at a certain moment contains $24$ stones they may take only $1,2,3,4,6,8$ or $12$ stones from that pile. So if a pile contains one stone they can't take the last stone from it as $1$ isn't a proper divisor of $1$. The first player that can't make a valid move loses the game. Of course both Anton and Bertrand play optimally.

The triple $(a,b,c)$ indicates the number of stones in the three piles. Let $S(n)$ be the number of winning positions for the next player for $1 ≤ a, b, c ≤ n$. $S(10) = 692$ and $S(100) = 735494$.

Find $S(123456787654321)$ modulo $1234567890$.