On the number of special numbers

AKTAŞ K., Murty M. R.

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, cilt.127, sa.3, ss.423-430, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 127 Sayı: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s12044-016-0326-z
  • Dergi Adı: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.423-430
  • Anahtar Kelimeler: Special numbers, squarefull numbers, Thue-Mahler equations, abc conjecture, ABC-CONJECTURE
  • Gazi Üniversitesi Adresli: Evet

Özet

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.