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On the sum \(\sum^x_{k=1} d(f(k))\). (English) Zbl 0046.04103

Let \(d(n)\) denote the number of divisors of a positive integer \(n\) and \(f(x)\) be a polynomial with integral coefficients. The author proves that \[ 0 < c_1 < \left(\varlimsup_{N \to \infty} \sum_{x=1}^N d(f(x)) \right)/N\log N < c_2 < \infty. \]
Reviewer: Loo-Keng Hua

MSC:

11N64 Other results on the distribution of values or the characterization of arithmetic functions
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