Best score in the divisor tax game on 1 to 10

The numbers $1$ through $10$ are written on a board. On each turn you claim one remaining number, and a tax collector immediately removes every remaining number that divides it (other than itself). You may only claim a number if at least one of its proper divisors is still on the board. When no legal move exists, the collector takes whatever is left. Your score is the sum of what you claimed. What is the highest score you can guarantee?

$40$. Only one prime can ever be claimed (all primes lose their only proper divisor $1$ at once), so take $7$ first. Then claim $9$ (losing $3$), $6$ (losing $2$), and then $8$ and $10$ (losing $4$ and $5$): you hold $6+7+8+9+10=40$, and an exhaustive search confirms nothing better is possible.