Multiperfect numbers on lines of the Pascal triangle

  1. Luca, F. 2
  2. Varona, J.L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad Nacional Autónoma de México
    info

    Universidad Nacional Autónoma de México

    Ciudad de México, México

    ROR https://ror.org/01tmp8f25

Revista:
Journal of Number Theory

ISSN: 0022-314X

Any de publicació: 2009

Volum: 129

Número: 5

Pàgines: 1136-1148

Tipus: Article

DOI: 10.1016/J.JNT.2008.10.003 SCOPUS: 2-s2.0-62349107107 WoS: WOS:000265753700013 GOOGLE SCHOLAR lock_openAccés obert editor

Altres publicacions en: Journal of Number Theory

Repositori institucional: lock_openAccés obert Postprint lockAccés obert Editor

Projectes relacionats

Ortogonalidad y aproximación: teoría y aplciaciones físicas y clínicas

2006/00095/001

Resum

A number n is said to be multiperfect (or multiply perfect) if n divides its sum of divisors σ (n). In this paper, we study the multiperfect numbers on straight lines through the Pascal triangle. Except for the lines parallel to the edges, we show that all other lines through the Pascal triangle contain at most finitely many multiperfect numbers. We also study the distribution of the numbers σ (n) / n whenever the positive integer n ranges through the binomial coefficients on a fixed line through the Pascal triangle.