Smallest palindrome with exactly $n$ divisors

formal-conjectures · oeis · ams-11

The sequence $a(n)$ is the smallest palindromic number with exactly $n$ divisors, or $0$
if no such number exists.

There are no palindromic numbers greater than 1 which are the fifth or higher power of a natural
number.

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://oeis.org/A083753
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/83753.lean
Local target: Corpus.OEIS83753.conjecture
Source SHA-256: b13eaa4f66fdc006fa804c80c809f04aac3baf8540310a0162bf983898a5ad40
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