JOURNAL ARTICLE

On the index of friability.

  • Published In: International Journal of Number Theory, 2025, v. 21, n. 6. P. 1395 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: De Koninck, Jean-Marie; Luca, Florian 3 of 3

Abstract

Given an integer n ≥ 2 , let P (n) stand for its largest prime factor, setting P (1) = 1. We introduce the arithmetic function fria (n) : = log n / log P (n) (with fria (1) = 1) and call it the index of friability of the integer n. The index of friability of an integer is an absolute measure of its friability (or smoothness). We first determine the respective mean values of the functions fria (n) and 1 / fria (n) , thereafter obtaining various estimates comparing the index of friability with the index of composition. Then, given any finite set of natural numbers, we order its members according to their index of friability and obtain results regarding their distribution. In particular, this allows us to construct arbitrarily long monotonic sequences of integers with increasing index of friability. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Number Theory. 2025/07, Vol. 21, Issue 6, p1395
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2025
  • ISSN:1793-0421
  • DOI:10.1142/S179304212550071X
  • Accession Number:185548017
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