Erdős, Pál On the sum \(\sum^x_{k=1} d(f(k))\). (English) Zbl 0046.04103 J. Lond. Math. Soc. 27, 7-15 (1952). 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 Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 37 Documents MSC: 11N64 Other results on the distribution of values or the characterization of arithmetic functions Keywords:number of divisors of a positive integer; polynomial with integral coefficients. PDFBibTeX XMLCite \textit{P. Erdős}, J. Lond. Math. Soc. 27, 7--15 (1952; Zbl 0046.04103) Full Text: DOI