Abstract
We use the saddle-point method (due to Hildebrand?Tenenbaum [3]) to study the asymptotic behavior of ?n?x, p(n)?y ?k(n) for any k > 0 fixed, where P(n) is the greatest prime factor of n and ?k is Piltz' function. We generalize all results in [3], where the case k = 1 has been treated.
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