A sieve problem and its application

Andreas Weingartner

Let $\theta$ be an arithmetic function and let $\mathcal{B}$ be the set of positive integers $n=p_1^{{\alpha }_1}\cdots p_k^{{\alpha }_k}$, which satisfy $p_{j+1} \le θ( p_1^{α_1}\cdots p_{j}^{α_{j}})…