Erdos Problem #1061
Let $S(x)$ count ordered pairs $(a,b)$ with $a+b \le x$ and $\sigma(a)+\sigma(b) = \sigma(a+b)$. Erdos asked whether $S(x) \sim cx$. The opposite extreme holds: for every $R > 0$, $S(x)/(x(\log x)^R) \to \infty$, so the count beats every fixed logarithmic scale.
Exact FrontierDelta
Scope and record
Occurred: Jun 24, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: Erdos Problem #1061 · Erdos 1061 · Problem 1061
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Eric Li
human · human collaborator
ChatGPT
model · ai model contributor · OpenAI / Harmonic
Aristotle
model · ai model contributor · OpenAI / Harmonic
Lineage and corrections
This event attributed to Eric Li
This event attributed to Aristotle
This event attributed to ChatGPT