  A sequence $A$ of positive integers having the property that no element $a_i
\in A$ divides the sum $a_j+a_k$ of two larger elements is said to have
`Property P'. We construct an infinite set $S\subset \mathbb{N}$ having
Property P with counting function $S(x)\gg\frac{\sqrt{x}}{\sqrt{\log
x}(\log\log x)^2(\log \log \log x)^2}$. This improves on an example given by
Erd\H{o}s and S\'ark\"ozy with a lower bound on the counting function of order
$\frac{\sqrt{x}}{\log x}$.
