Let $f (n)$ count the number of solutions to $k σ (k) = n$ , where $σ (k)$ is the sum of divisors of $k$ . Is it true that $f (n) \leq n^{o (\frac{1}{l o g l o g n})}$ ? Perhaps even $\leq (lo g n)^{O (1)}$ ?

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

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

Let [ A(k):=k\sigma(k),\qquad f(n)=|\\{k\in\mathbb N:\ A(k)=n\\}|. ]

llm-hunter · gpt pro 5.2 · unverified

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

AMS 11 · open (literature)

theorem erdos_1060.parts.i :
    ∃ h : ℕ → ℝ,
      h =o[atTop] (fun n ↦ 1 / log (log n)) ∧ ∀ᶠ n in atTop, #{k ≤ n | k * σ 1 k = n} ≤ (n : ℝ) ^ h n

open