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erdős #534

← #533 · #535 → (packet.json; erdosproblems.com)

What is the largest possible subset $A \subseteq {1, \dots, N}$ which contains $N$ such that $gcd (a, b) > 1$ for all $a \neq = b \in A$ ?

Worked, still open.

number theory · solved · 0 attempts

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A387543 — a(n) is the size of the largest subset of {1, 2, ..., n} containing n in which any two numbers share a prime factor.1,1,1,2,1,3,1,4,3,5,1,6,1,7,5,8,1,9,1,10,7,11,1,12,5,13,9,14,1,15,1,16,11,17,7,18,1,19,13,20,1,21,1,22,15,23,1,24,7,25,1 A387698 — Irregular triangle read by rows in which row n is the maximum clique containing n in the gcd-graph of {1, 2, ..., n}. If more than one such clique exists, choose the lexicographically earliest.1,2,3,2,4,5,2,4,6,7,2,4,6,8,3,6,9,2,4,6,8,10,11,2,4,6,8,10,12,13,2,4,6,8,10,12,14,3,6,9,12,15,2,4,6,8,10,12,14,16,17,2,4

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solved

finding.noted · reviewer:will-blair · 1 day

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