Geodesic
Additive problems for integers with a given number of prime divisors
Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 749-762

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The asymptotics of sums of the form $\sum_{\substack n$ (summation over $n$, $\omega(n)=k$) is studied, where $\omega(n)$ is the number of distinct prime divisors of $n$, and $\tau(n)$ is the number of all divisors. 
@article{MZM_1998_63_5_a13,
     author = {M. B. Khripunova},
     title = {Additive problems for integers with a given number of prime divisors},
     journal = {Matemati\v{c}eskie zametki},
     pages = {749--762},
     publisher = {mathdoc},
     volume = {63},
     number = {5},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a13/}
}
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M. B. Khripunova. Additive problems for integers with a given number of prime divisors. Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 749-762. http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a13/