Sumsets avoiding squarefree integers
  We describe the structure of a set of integers $A$ of positive density $\delta$, such that $A+A$ contains no squarefree integer. It turns out that the behaviour changes abruptly at the values $\delta_0=1/4-\frac{2}{\pi^2}=0.0473...$ and $\delta_1=1/18$. 
Jan-Christoph Schlage-Puchta
math.NT