Positive correlation with the sequence $\sqrt{ij}/2-\min(i,j)$

202 Views Asked by At

Is there a sequence of positive real numbers $x_1,\ldots,x_n$ for which $$ \sum_{1\leq i,j\leq n}\left[\frac{\sqrt{ij}}{2}-\min(i,j)\right]x_ix_j> 0? $$