Erdős Problem 1060

formal-conjectures · erdos-problems · ams-11

The conjecture is about the function $f(n)$ which counts the number of solutions to
$k\sigma(k)=n$, where $\sigma(k)$ is the sum of divisors of $k$. The first bound is that $f(n)$ grows slower
than any power of $n^(\frac{1}{\log\log n})$. The second bound is that $f(n)$ is at most a power of
$\log n$.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.erdosproblems.com/1060
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/ErdosProblems/1060.lean
Local target: Corpus.Erdos1060.erdos_1060.parts.i
Source SHA-256: 7eea6419d8ebd50bc1e6919b48aef8f295aec0a93ca51654599fbf49301d398b
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record