Geodesic
The Ingham Divisor Problem on the Set of Numbers without $k$h Powers
Matematičeskie zametki, Tome 69 (2001) no. 3, pp. 383-401

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Suppose that $k$ and $l$ are integers such that $k\ge2$ and $l\ge2$ , $M_k$ is a set of numbers without $k$th powers, and $\tau(n)=\sum_{d\mid n}1$. In this paper, we obtain asymptotic estimates of the sums $\sum\tau(n)\tau(n+1)$ over $n\le x$, $n\in M_k$. 
@article{MZM_2001_69_3_a7,
     author = {T. K. Ikonnikova},
     title = {The {Ingham} {Divisor} {Problem} on the {Set} of {Numbers} without $k$h {Powers}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {383--401},
     publisher = {mathdoc},
     volume = {69},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a7/}
}
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T. K. Ikonnikova. The Ingham Divisor Problem on the Set of Numbers without $k$h Powers. Matematičeskie zametki, Tome 69 (2001) no. 3, pp. 383-401. http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a7/