I have to prove $$\sum_{n=1}^N\lambda(n)[N/n]=[\sqrt{N}]$$ I tried using the approach in this question but I don't know how I'll get $\sqrt{N}$. Please help.
2026-03-25 15:58:42.1774454322
$\sum_{n=1}^N\lambda(n)[N/n]=[\sqrt{N}]$ Identity involving Liouville Lambda function
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HINT
$$\sum_{n=1}^N\lambda(n)[N/n] =\sum_{n=1}^N\sum_{d|n}\lambda(d) $$
Next use this to conclude that the double sum equals the number of perfect squares not exceeding $N$