Bounds the weighted sum $\sum 1/(a \log a)$ taken over primitive sets of integers (sets where no element divides another).

Is it true that, for any $x$, if $A\subset [x,\infty)$ is a primitive set of integers (so that no distinct elements of $A$ divide each other) thenUnparsed notation: \sum_{a\in A}\frac{1}{a\log a}< 1+o(1),where the $o(1)$ term $\to 0$ as $x\to \infty$? -