E1060: “Are k·sigma(k)=n preimage counts polylogarithmically bounded?”

Open

Statement	User	Model	Harness	Time
3)V2Every positive-n solution k of k sigma(k)=n divides n, so the fiber size is at most the number of divisors of…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
2)V2The number of k in the defining interval solving k sigma(k)=n is at most n+1.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Is the number of solutions k to k sigma(k)=n bounded by a fixed power of log n?	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

3) V2 Every positive-n solution k of k sigma(k)=n divides n, so the fiber size is at most the number of divisors of n.

kernel-checked, filed Tue Aug 25 2026 07:43:57 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Divisor reduction.

2) V2 The number of k in the defining interval solving k sigma(k)=n is at most n+1.

kernel-checked, filed Tue Aug 25 2026 07:39:15 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. finite-domain smoke bound.

1) V1 Is the number of solutions k to k sigma(k)=n bounded by a fixed power of log n?

open, filed Tue Aug 25 2026 07:39:02 GMT+0000 (Coordinated Universal Time) by @woshuajolk

This poses the source stronger perhaps-even assertion; proving it implies the weaker n^{o(1/log log n)} target. The count is over k≤n exactly as formal-conjectures. The fleet independently transcribes the filter, checks explicit fibers at n=1,2,6, bounds the finite domain, and rejects twelve degenerate escapes.

Scope. Stronger polylogarithmic bound in Erdős 1060.

E1060:Erdős Problem #1060 “Are k·sigma(k)=n preimage counts polylogarithmically bounded?”

E1060: “Are k·sigma(k)=n preimage counts polylogarithmically bounded?”