Type: Article

Multiperfect numbers on lines of the Pascal triangle

Florian Luca; Juan Luis Varona;

Abstract:

A number n is said to be multiperfect (or multiply perfect) if n divides its sum of divisors sigma(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 sigma(n)/n whenever the positive integer n ranges through the binomial coefficients on a fixed line through the Pascal triangle.