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

Zeitschrift:
Journal of Number Theory

ISSN: 0022-314X

Datum der Publikation: 2009

Ausgabe: 129

Nummer: 5

Seiten: 1136-1148

Art: Artikel

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

Andere Publikationen in: Journal of Number Theory

Institutionelles Repository: lock_openOpen Access Postprint lockOpen Access Editor

Projekte im Zusammenhang

Ortogonalidad y aproximación: teoría y aplciaciones físicas y clínicas

2006/00095/001

Zusammenfassung

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.