Numerator of $1/\det(M)$ for $M[i,j] = 1/\operatorname{lcm}(i,j)$

formal-conjectures · oeis · ams-11 · ams-15

Numerator of $1/\det(M)$ where $M$ is the $n \times n$ matrix with
$M[i,j] = 1/\operatorname{lcm}(i,j)$.

"Conjecture: $1/\det(M)$ is an integer only for n: 1 to 34, 36 and 38.
All denominators are powers of two (A000079). - _Robert G. Wilson v_, Aug 02 2015"

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/A060841
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/60841.lean
Local target: Corpus.OEIS60841.conjecture
Source SHA-256: 84f3d71cc53d740bef0a2bb52bf5c9a867b4f057e9fd9461ef31e5db49bf9173
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