On a Problem of Erdos Involving the Largest Prime Factor of n

• Autores: Aleksandar Ivic
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 145, Nº 1, 2005, págs. 35-46
• Idioma: inglés
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• Resumen

  • Let P(n) denote the largest prime factor of an integer n (2), and let N (x) denote the number of natural numbers n such that 2 n x, and n does not divide P(n)!. We prove that where (u) is the Dickman-de Bruijn function. In terms of elementary functions we have thereby sharpening and correcting recent results of K. Ford and J.-M. De Koninck and N. Doyon.