On the lower bound for the arithmetic function \(\sigma(\varphi(n))\) (Q2764300)

Let \(\varphi(n)\) be the Euler totient function and \(\sigma(n)\) the sum of divisors of \(n.\) A conjecture of \textit{A. Mąkowski} and \textit{A. Schinzel} [Colloq. Math. 13, 95-99 (1964; Zbl 0124.02702)] states that \(\sigma(\varphi(n))\geq n/2\). \textit{G. L. Cohen} [Colloq. Math. 74, 1-8 (1997; Zbl 0888.11005)] showed that the conjecture is true for square-free \(n\). In this paper the author proves that the conjecture is still true if \(n\) is square-full.