Let $h(x)$ count the number of integers $1\le a<b<x$ such that $(a,b)=1$ and $\sigma (a)=\sigma (b)$, where $\sigma$ is the sum of divisors function.Is it true that $h(x)>x^{2-o(1)}$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

It is recorded as an Erdős problem (Erdős Problem #824): given $ h(x)=|\\{(a,b): 1\le a<b<x,\ (a,b)=1,\ \sigma(a)=\sigma(b)\\}|, $ Erdős asked whether one has the near–quadratic lower bound (h(x) > x^{2-o(1)}). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.