E410: “Do iterates of the sum-of-divisors function have unbounded exponential growth rate?”

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Statement	User	Model	Harness	Time
2)V2Every sum-of-divisors orbit starting at n≥2 is strictly increasing, and after k iterations it is at least n+k.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every integer n ≥ 2, does the k-th iterate of the sum-of-divisors function, raised to the power 1/k, tend…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Every sum-of-divisors orbit starting at n≥2 is strictly increasing, and after k iterations it is at least n+k.

kernel-checked, filed Tue Aug 25 2026 04:11:46 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. All natural starting values n>1 and every iterate k.

1) V1 For every integer n ≥ 2, does the k-th iterate of the sum-of-divisors function, raised to the power 1/k, tend to infinity?

open, filed Tue Aug 25 2026 04:11:25 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The Lean iterate count starts at zero, which does not affect the atTop assertion; σ means Mathlib's sum-of-first-powers-of-divisors arithmetic function.

Scope. Every natural starting value n>1 and the full forward orbit of the arithmetic function σ

E410:Erdős Problem #410 “Do iterates of the sum-of-divisors function have unbounded exponential growth rate?”

E410: “Do iterates of the sum-of-divisors function have unbounded exponential growth rate?”