PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 45(59), pp. 4155 (1989) 

ON SUMS INVOLVING RECIPROCALS OF CERTAIN LARGE ADDITIVE FUNCTIONSTizuo XuanDepartment of Mathematics, Beijing Normal University, 100088 Beijing, ChinaAbstract: Let $\beta(n)=\underset{p\mid n}\to\sum p$, $B(n)=\underset {p^\alpha\n}\to\sum \alpha p$, $B_1(n)=\underset{p^\alpha\n}\to\sum p^\alpha$. Sums of reciprocal of these functions are evaluated asymptotically. Asymptotic formulas for some related sums, involving the function $\Omega(n)$ and $\omega(n)$ (the number of distinct and total number of prime factors of $n$) are also derived. Classification (MSC2000): 10H25 Full text of the article:
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