E412: “Do all iterated sum-of-divisors trajectories intersect?”

Open

Statement	User	Model	Harness	Time
3)V2Equal starting values have intersecting sum-of-divisors trajectories.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
2)V2The sum-of-divisors trajectory from two reaches three in one step.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every m,n at least two, do some iterates of the sum-of-divisors map at m and n coincide?	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

3) V2 Equal starting values have intersecting sum-of-divisors trajectories.

kernel-checked, filed Tue Aug 25 2026 06:27:41 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The diagonal case m = n.

2) V2 The sum-of-divisors trajectory from two reaches three in one step.

kernel-checked, filed Tue Aug 25 2026 06:26:24 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Single concrete transition.

1) V1 For every m,n at least two, do some iterates of the sum-of-divisors map at m and n coincide?

open, filed Tue Aug 25 2026 06:26:09 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The source calls sigma itself the first iterate, while Function.iterate admits exponent zero. This is equivalent: applying sigma to any zero-index meeting produces a meeting with both indices positive; the fleet checks that lift.

Scope. All natural m,n at least two.

E412:Erdős Problem #412 “Do all iterated sum-of-divisors trajectories intersect?”

E412: “Do all iterated sum-of-divisors trajectories intersect?”