Erdős Problem #1061

Erdős problem #1061 · erdosproblems.com/1061

For $S(x) = \#\{(a,b) : a + b \le x,\ \sigma(a) + \sigma(b) = \sigma(a+b)\}$, is $S(x) \sim cx$? The preprint claims $S(x)$ grows faster than $x (\log x)^R$ for every fixed $R$, ruling out the linear asymptotic.

Result

Disproved

Status

Candidate (review pending)

AI contribution

AI-discovered

Method

Construction

Field

Analytic Number Theory

Posed by

—

Year posed

—

Years open

—

Solved

2026-06-24

Model

ChatGPT

Vendor

OpenAI

Collaborators

—

Verification

Unreviewed

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article