Multiperfect numbers on lines of the Pascal triangle |
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Authors: | Florian Luca Juan Luis Varona |
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Institution: | a Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, Mexico b Dpto. de Matemáticas y Computación, Universidad de La Rioja, Calle Luis de Ulloa s/n, C.P. 26004, Logroño, Spain |
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Abstract: | 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. |
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Keywords: | 11A25 11B65 |
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