Claims

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2004_06_30_konyagin: Konyagin's 2004 bound on the largest subset of [1,N] with squarefree sums, N^{11/15} times a subexponential factor, gives a_j >> j^{15/11-o(1)} for every infinite set with squarefree sums; refereed.

2025_11_30_van_doorn_tao: Van Doorn and Tao's first arXiv version (2025): every infinite set with squarefree sums has a_j >> j^{4/3}, and some squarefree such set has a_j <= exp(Cj/log j); the true growth rate is not settled.

2026_07_23_hu: Hu's July 2026 note constructs an infinite set with squarefree pairwise sums, doubles included, and counting function of order at least (log x)^2, so a_j is at most exp(C sqrt j), with a partial Lean 4 development.

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