Problem 648

Let $g(n)$ denote the largest $t$ such that there exist integers $2\leq a_1<a_2<\cdots <a_t <n$ such that

P(a_1)>P(a_2)>\cdots >P(a_t)

where $P(m)$ is the greatest prime factor of $m$ . Estimate $g(n)$ .

Source: erdosproblems.com/648

Number theory

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An accepted solution exists. Settled in another form, for example when its parts resolve differently or the question is open-ended.

Solved; the site's label is SOLVED (LEAN). Cambie's 2025 paper gives the order of growth, and the site's Lean label follows the formalization of his proof announced in the site's thread on 2026-02-04, a Lean 4 development that this corpus has not built or audited, so it gives no formalized evidence; see the claim page (Cambie, 2025).

Problem 648

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