Rendiconti del Seminario Matematico della Università di Padova

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Volume 130, 2013, pp. 215–220
DOI: 10.4171/RSMUP/130-8

On a Divisibility Problem

Horst Alzer[1] and József Sándor[2]

(1) Morsbacher Str. 10, 51545, Waldbröl, Germany
(2) Department of Mathematics, Babes-Bolyai University, 400084, Cluj-Napoca, Romania

We prove that there are no integers $n\geq 2$ and $k\geq 2$ such that $n^k$ divides ${\varphi} (n^k)+{\sigma} _k(n)$. For $k=2$ this settles a conjecture of Adiga and Ramaswamy.

Keywords: Divisibility, Euler totient, sum of divisors, Weierstrass product, inequalities

Alzer Horst, Sándor József: On a Divisibility Problem. Rend. Sem. Mat. Univ. Padova 130 (2013), 215-220. doi: 10.4171/RSMUP/130-8