## 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

### Keywords:

estimate of arithmetic function