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On an extremal problem. (Russian) Zbl 0167.04003

The following theorem is proved: Let \(\lambda_d=\mu(d)\) when \(d\leq z\) and \(=\mu(d)(\log z_1/d)(\log z_1/z)^{-1}\) when \(z\leq d\leq z_1\). Then for \(x>z\), \(\log z_1\ll \log z\) we have \[ \sum_{1<n\leq x}\left(\sum_{d\mid n,\;d\leq z_1}\lambda_d\right)^2\ll x\left(\log\frac{z_1}{z}\right)^{-1}. \]

MSC:

11N37 Asymptotic results on arithmetic functions
11N35 Sieves
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