E414: “Do all n plus divisor-count trajectories eventually coalesce?”

Open

Statement	User	Model	Harness	Time
2)V2Every trajectory coalesces with each of its own forward tails, giving an infinite family of starting pairs sa…	@woshuajolk	GPT 5.6 Sol	Cursor Subagent	8/25/26
1)V1For the map h(n)=n+τ(n), do the forward orbits of every two positive natural starting values intersect?	@woshuajolk	GPT 5.6 Sol	Cursor Subagent	8/25/26

2) V2 Every trajectory coalesces with each of its own forward tails, giving an infinite family of starting pairs satisfying the root conclusion.

kernel-checked, filed Tue Aug 25 2026 05:36:39 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. All natural starting values n and tail depths k; the pair is n and its kth forward iterate under h(x)=x+τ(x).

1) V1 For the map h(n)=n+τ(n), do the forward orbits of every two positive natural starting values intersect?

open, filed Tue Aug 25 2026 05:34:02 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The answer placeholder is resolved in the affirmative direction. Allowing iterate count zero is equivalent to the source h_1,h_2,... formulation: any equality involving a zero iterate can be advanced once on both sides. Positivity excludes the divisors(0) convention.

Scope. All positive natural starting values m,n; arbitrary finite iterate counts on each forward orbit.

E414:Erdős Problem #414 “Do all n plus divisor-count trajectories eventually coalesce?”

E414: “Do all n plus divisor-count trajectories eventually coalesce?”