Claims

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1984_01_01_erdos_van_lint: Erdős states in 1984, without proof, that for large n an optimal admissible set must contain an element that is not a prime power, the second question at k = 2; the site credits the result to Erdős and van Lint.

2026_09_06_kitamura: Kitamura's 2026 Lean development, made with OpenAI Codex and ChatGPT Astra, proves that for large n every element of every optimal admissible set has at most two distinct prime factors, so the second question fails at k = 3.

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