Let $f (n)$ be the size of the largest subset $A \subseteq {1, \dots, n}$ such that there are no three distinct elements $a, b, c \in A$ such that $a ∣ b$ and $a ∣ c$ . How large can $f (n)$ be? Is $lim f (n) / n$ irrational?

Open — best to date is a honest null, not yet sealed.

number theory · open · formalized (Lean) · 1 attempt

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

honest null

needs verification

attempted via frontier '?' (transfer_strength=n/a) -> no_progress

No solve/partial on this pass. Transfer into the owned frontier was 'n/a'. Do not re-attack cold; needs a new idea or richer accumulated context.

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let (A\subseteq{1,\dots,n}). Your condition says:

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 11 · open (literature)

theorem erdos_1062.parts.ii :
    (∃ l, Tendsto (fun n => (f n : ℝ) / n) atTop (𝓝 l) ∧ Irrational l) ↔ answer(sorry)

open