Geodesic
On Sums Involving Reciprocals of Certain Large Additive Functions
Publications de l'Institut Mathématique, _N_S_45 (1989) no. 59, p. 41 .

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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 : 10H25 
@article{PIM_1989_N_S_45_59_a6,
     author = {Tizuo Xuan},
     title = {On {Sums} {Involving} {Reciprocals} of {Certain} {Large} {Additive} {Functions}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {41 },
     publisher = {mathdoc},
     volume = {_N_S_45},
     number = {59},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1989_N_S_45_59_a6/}
}
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Tizuo Xuan. On Sums Involving Reciprocals of Certain Large Additive Functions. Publications de l'Institut Mathématique, _N_S_45 (1989) no. 59, p. 41 . http://geodesic.mathdoc.fr/item/PIM_1989_N_S_45_59_a6/