Source labels openChecked July 26, 2026

No powers as partition numbers

There are no partition numbers $a(k)$ of the form $x^m$ , with $x,m$ integers $>1$ . See comment by Zhi-Wei Sun (Dec 02 2013).

Number theory AMS 11

Mathematical statement

There are no partition numbers $a(k)$ of the form $x^m$ , with $x,m$ integers $>1$ . See comment by Zhi-Wei Sun (Dec 02 2013).

Statement source: OEIS statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

noPowerPartitionNumber

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem noPowerPartitionNumber : answer(sorry) ↔ ∀ k, ¬IsPerfectPower (a k) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization A41background