Brainteaser - The Taxman’s Table

Numbers 1 through n lie on a table. You may pick a number x only if at least one of its proper divisors is still on the table. You keep x, and the Taxman instantly removes (keeps) all of x’s proper divisors that remain on the table. The game ends when no legal move remains; any leftover numbers go to the Taxman. For general n, devise a strategy that maximizes your total and explain why it works.