Numerator - denominator in $n$-th harmonic number

formal-conjectures · oeis · ams-11

$a(n) = \text{numerator}(H_n) - \text{denominator}(H_n)$, where
$H_n = 1 + 1/2 + \dots + 1/n$.

"Conjecture: for $n > 2$, $n$ divides $a(n-2)$ if and only if $n$ is a prime.
Checked up to 20000. - _Amiram Eldar_ and _Thomas Ordowski_, Jul 27 2019"

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/A064169
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/64169.lean
Local target: Corpus.OEIS64169.conjecture
Source SHA-256: 8deefea47fa137e7863052b7d254b978e4f48387f3cbb9cfdb7cbb8196bdeefc
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