Number of different products of subsets of $\{1, 2, \dots, n\}$

formal-conjectures · oeis · ams-5 · ams-11

The number of distinct products (including the empty product 1) of any subset
of $\{1, 2, \dots, n\}$.

Conjecture: let $p \le n$ be prime. If $m$ and $p^a m$ are two such products, then so is $p^k m$
for all $0 < k < a$.
- Yan Sheng Ang, Feb 13 2020

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/A060957
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/60957.lean
Local target: Corpus.OEIS60957.conjecture
Source SHA-256: 0ca844760edbe5e331a50e65743990e3720b213a73e216cdf66561ad564e802a
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