## Nonaliquots and Robbins Numbers

Banks, William David, 1964-

Luca, Florian

##### Abstract

Let '(•) and _(•) 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 = _(n)−n has no solution. We also show that the set of positive integers m not of the form (p − 1)/2 − '(p − 1) for some prime number p has a positive lower asymptotic density.

##### Part of

Mathematics publications (MU)

##### Citation

Colloq. Math., 103 (2005), 27-32.