For a positive integer n, let σ(n) denote the sum of the positive divisors of n. We call n a near-perfect number if σ(n) = 2n + d where d is a proper divisor of n. We show that the only odd near-perfect number with four distinct prime divisors is 3⁴·7²·11²·19².
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6588-10-2015,
author = {Min Tang and Xiaoyan Ma and Min Feng},
title = {On near-perfect numbers},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {157-188},
zbl = {06574998},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6588-10-2015}
}
Min Tang; Xiaoyan Ma; Min Feng. On near-perfect numbers. Colloquium Mathematicae, Tome 144 (2016) pp. 157-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6588-10-2015/