Outsmarting the Auditor

Cards numbered $1$ through $n$ lie face-up on a desk. You play against an auditor under one rule: you may claim card $x$ only while at least one proper divisor of $x$ is still on the desk. The instant you claim $x$, the auditor confiscates every proper divisor of $x$ that remains. Play stops when you have no legal claim left, and the auditor pockets everything still on the desk. For a general $n$, describe a strategy that makes your total as large as possible, and explain the reasoning behind it.