$\gcd(\mathrm{numerator}(H_n), n!)$

formal-conjectures · oeis · ams-11

$a(n) = \gcd(\mathrm{A001008}(n), n!)$, where $\mathrm{A001008}(n)$ is the numerator of
the $n$-th harmonic number $H_n = \sum_{i=1}^n \frac{1}{i}$.

Conjecture: Every odd prime occurs as a term in the sequence.

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/A093818
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/93818.lean
Local target: Corpus.OEIS93818.conjecture
Source SHA-256: 51fdc7188947ebaf77f21fd03675fdc5a3ee23d8344f1af008f5feebe46ed69d
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