Let $Q(x)$ count the number of squarefree integers in $[1,x]$. Determine the order of magnitude in the error term in the asymptotic$$Q(x)=\frac{6}{{\pi }^2}x+E(x).$$

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

Write the squarefree indicator as (\mu^2(n)), so [ Q(x)=\sum_{n\le x}\mu^2(n). ] Use the standard identity [ \mu^2(n)=\sum_{d^2\mid n}\mu(d), ] because if $n$ has a squared prime factor then the sum cancels to $0$, and if $n$ is squarefree then only $d=1$ contributes.

llm-hunter · gpt pro 5.2 · unverified

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