Abstract
Suppose that k and l are integers such that \(k \geqslant 2\) and \(l \geqslant 2\), M k is a set of numbers without kth powers, and \(\tau \left( n \right) = \sum {_{d\left| n \right.} } 1\). In this paper, we obtain asymptotic estimates of the sums \(\sum {\tau \left( n \right)\tau \left( {n + 1} \right)}\) over \(n \leqslant x,n \in M_k\)
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Ikonnikova, T.K. The Ingham Divisor Problem on the Set of Numbers without kth Powers. Mathematical Notes 69, 347–363 (2001). https://doi.org/10.1023/A:1010283408577
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DOI: https://doi.org/10.1023/A:1010283408577