On near-perfect and deficient-perfect numbers

Min Tang, Xiao-Zhi Ren, and Meng Li. "On near-perfect and deficient-perfect numbers." Colloquium Mathematicae 133.2 (2013): 221-226. <http://eudml.org/doc/284301>.

@article{MinTang2013,
abstract = {For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n. We call n a near-perfect number if σ(n) = 2n + d, and a deficient-perfect number if σ(n) = 2n - d. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.},
author = {Min Tang, Xiao-Zhi Ren, Meng Li},
journal = {Colloquium Mathematicae},
keywords = {near-perfect number; deficient-perfect number; divisor-sum-function},
language = {eng},
number = {2},
pages = {221-226},
title = {On near-perfect and deficient-perfect numbers},
url = {http://eudml.org/doc/284301},
volume = {133},
year = {2013},
}

TY - JOUR
AU - Min Tang
AU - Xiao-Zhi Ren
AU - Meng Li
TI - On near-perfect and deficient-perfect numbers
JO - Colloquium Mathematicae
PY - 2013
VL - 133
IS - 2
SP - 221
EP - 226
AB - For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n. We call n a near-perfect number if σ(n) = 2n + d, and a deficient-perfect number if σ(n) = 2n - d. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.
LA - eng
KW - near-perfect number; deficient-perfect number; divisor-sum-function
UR - http://eudml.org/doc/284301
ER -