Geodesic
On a conjecture of Mąkowski and Schinzel concerning the composition of the arithmetic functions σ and ϕ
Colloquium Mathematicum, Tome 86 (2000) no. 1, pp. 31-36.

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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.
DOI : 10.4064/cm-86-1-31-36

A. Grytczuk 1 ; F. Luca 1 ; M. Wójtowicz 1

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A. Grytczuk; F. Luca; M. Wójtowicz. On a conjecture of Mąkowski and Schinzel concerning the composition of the arithmetic functions σ and ϕ. Colloquium Mathematicum, Tome 86 (2000) no. 1, pp. 31-36. doi : 10.4064/cm-86-1-31-36. http://geodesic.mathdoc.fr/articles/10.4064/cm-86-1-31-36/

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