For any positive integer n let ϕ(n) and σ(n) be the Euler function of n and the sum of divisors of n, respectively. In [5], Mąkowski and Schinzel conjectured that the inequality σ(ϕ(n)) ≥ n/2 holds for all positive integers n. We show that the lower density of the set of positive integers satisfying the above inequality is at least 0.74.
@article{bwmeta1.element.bwnjournal-article-cmv86i1p31bwm,
author = {A. Grytczuk and F. Luca and M. W\'ojtowicz},
title = {On a conjecture of Makowski and Schinzel concerning the composition of the arithmetic functions s and ph},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {31-36},
zbl = {0965.11004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p31bwm}
}
Grytczuk, A.; Luca, F.; Wójtowicz, M. On a conjecture of Mąkowski and Schinzel concerning the composition of the arithmetic functions σ and ϕ. Colloquium Mathematicae, Tome 84/85 (2000) pp. 31-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p31bwm/
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