PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 46(60), pp. 2532 (1989) 

On sums involving reciprocals of certain large additive functions (II)Tizuo XuanDepartment of Mathematics, Beijing Normal University, 100088 Beijing, ChinaAbstract: Let $\beta(n)=\sum_{p\mid n}p$ and $B(n)=\sum_{p^{\alpha}\parallel n}\alpha p$. Let $p(n)$ denote the largest prime factor of an integer $n\ge2$. In the present paper we sharpen the asymptotic formula for the sum $\sum\limits_{2\le n\le x} B(n)/\beta(n)$ and we derive an asymptotic formula for the sum $\sum\limits_{2\le n\le x}(B(n)\beta(n))/p(n)$. Classification (MSC2000): 10H15; 10H25 Full text of the article:
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