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 $\operatorname{ES}_N$. 
@article{IM2_2004_68_3_a4,
     author = {S. V. Konyagin},
     title = {Problems on the set of squarefree numbers},
     journal = {Izvestiya. Mathematics },
     pages = {493--520},
     publisher = {mathdoc},
     volume = {68},
     number = {3},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a4/}
}
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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/