Nonaliquots and Robbins numbers

William D. Banks, and Florian Luca. "Nonaliquots and Robbins numbers." Colloquium Mathematicae 103.1 (2005): 27-32. <http://eudml.org/doc/284093>.

@article{WilliamD2005,
abstract = {Let φ(·) and σ(·) denote the Euler function and the sum of divisors function, respectively. 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.},
author = {William D. Banks, Florian Luca},
journal = {Colloquium Mathematicae},
keywords = {sum of divisors; Euler's totient function; aliquot number; nonaliquot numbers; lower asymptotic density of integers},
language = {eng},
number = {1},
pages = {27-32},
title = {Nonaliquots and Robbins numbers},
url = {http://eudml.org/doc/284093},
volume = {103},
year = {2005},
}

TY - JOUR
AU - William D. Banks
AU - Florian Luca
TI - Nonaliquots and Robbins numbers
JO - Colloquium Mathematicae
PY - 2005
VL - 103
IS - 1
SP - 27
EP - 32
AB - Let φ(·) and σ(·) denote the Euler function and the sum of divisors function, respectively. 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.
LA - eng
KW - sum of divisors; Euler's totient function; aliquot number; nonaliquot numbers; lower asymptotic density of integers
UR - http://eudml.org/doc/284093
ER -