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For an integer n, let d(n) denote the ordinary divisor function. This paper studies the asymptotic behavior of the sum
It is proved in the paper that, as x → ∞,
where A 1 and A 2 are certain constants and ε is any fixed positive real number.
The result corrects a false formula given in a paper of Gafurov concerning the same problem, and improves the error claimed by Gafurov.
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