Geodesic
Problems on the set of squarefree numbers
Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 493-520.

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Let $N$ be a positive integer and $\operatorname{ES}_N$ the maximal cardinality of a subset $\mathscr A\subset\{1,\dots,N\}$ such that $a+a'$ is squarefree for all $a\in\mathscr A$, $a'\in\mathscr A$. For large $N$ we obtain new upper and lower bounds for $\operatorname{ES}_N$. 
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S. V. Konyagin. Problems on the set of squarefree numbers. Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 493-520. http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a4/

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