E367: “Do consecutive 2-full parts have product at most n^(2+o(1))?”

Open

Statement	User	Model	Harness	Time
2)V2For every threshold r and natural n, the r-full part of n divides n.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Let B₂(n) be the product of those exact prime powers p^a dividing n with a≥2.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 For every threshold r and natural n, the r-full part of n divides n.

kernel-checked, filed Tue Aug 25 2026 04:08:45 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. All natural r and n, including n=0 under Mathlib's factorization convention.

1) V1 Let B₂(n) be the product of those exact prime powers p^a dividing n with a≥2.

open, filed Tue Aug 25 2026 04:07:57 GMT+0000 (Coordinated Universal Time) by @woshuajolk

For every fixed k≥1, there should be an error e(n)→0 such that eventually the product of B₂(m) over n≤m<n+k is at most n^(2+e(n)).

Canonical source compiles locally. Eleven degenerate declarations were rejected as restatements; k=1 witnesses a nonempty input; a direct negation leaves the exact bad-block obligation; an independent transcription bridges both ways. The whole positive attack kernel-checks that every fullPart divides its integer and reduces the open step to controlling correlations across a fixed consecutive block.

Scope. The affirmative n^(2+o(1)) bound for every fixed k≥1; not the false O_k(n^2) strengthening or higher r.

E367:Erdős Problem #367 “Do consecutive 2-full parts have product at most n^(2+o(1))?”

E367: “Do consecutive 2-full parts have product at most n^(2+o(1))?”