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erdős #648

← #647 · #649 → (packet.json; erdosproblems.com)

Let $g (n)$ denote the largest $t$ such that there exist integers $2 \leq a_{1} < a_{2} < \dots < a_{t} < n$ such that $P (a_{1}) > P (a_{2}) > \dots > P (a_{t})$ where $P (m)$ is the greatest prime factor of $m$ . Estimate $g (n)$ .

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number theory · solved · 0 attempts

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A391750 — Maximum length of an increasing sequence, bounded by n, in which the largest prime divisors of the elements form a decreasing sequence.1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,7,

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