If n is a positive integer such that ϕ(n)σ(n) = m² for some positive integer m, then m ≤ n. We put m = n-a and we study the positive integers a arising in this way.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-1-11,
author = {Kevin Broughan and Kevin Ford and Florian Luca},
title = {On square values of the product of the Euler totient and sum of divisors functions},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {127-137},
zbl = {1286.11005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-1-11}
}
Kevin Broughan; Kevin Ford; Florian Luca. On square values of the product of the Euler totient and sum of divisors functions. Colloquium Mathematicae, Tome 131 (2013) pp. 127-137. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-1-11/