Chandler S. Robbins, 1918–2017

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The Robbins Equation

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Let φ(·) and σ(·) denote the Euler function and the sum of divisors function, respectively. In this paper, we give a lower bound for the number of m ≤ x for which the equation m = σ(n)−n has no solution. We also show that the set of positive integers m not of the form (p − 1)/2 − φ(p − 1) for some prime number p has a positive lower asymptotic density. ∗MSC numbers: 11A25; 11A41, 11N64

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ژورنال

عنوان ژورنال: The Auk

سال: 2017

ISSN: 0004-8038,1938-4254

DOI: 10.1642/auk-17-140.1