On a conjecture of Mąkowski and Schinzel concerning the composition of the arithmetic functions σ and ϕ
Volume 86 / 2000
Colloquium Mathematicum 86 (2000), 31-36
DOI: 10.4064/cm-86-1-31-36
Abstract
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.
