On the number of special numbers


AKTAŞ K. , Murty M. R.

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, vol.127, no.3, pp.423-430, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 127 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.1007/s12044-016-0326-z
  • Title of Journal : PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
  • Page Numbers: pp.423-430

Abstract

For lack of a better word, a number is called special if it has mutually distinct exponents in its canonical prime factorizaton for all exponents. Let V(x) be the number of special numbers <= x. We will prove that there is a constant c > 1 such that V(x) similar to cx/log x. We will make some remarks on determining the error term at the end. Using the explicit abc conjecture, we will study the existence of 23 consecutive special integers.