On the composition of a certain arithmetic function (Q1048677)

The main subject of the paper under review is studying the arithmetic function \(S:\mathbb{N}\to\mathbb{N}\) defined by \(S(n)=\min\{m: n|m!\}\). The authors start their work by reviewing and obtaining some properties of \(S(n)\), and then they obtain various inequalities involving the function \(S(f(n))\) for some arithmetic functions \(f\) including the Euler function and the sum of divisors function. They also investigate the values of \(S(F_n)\) and \(S(L_n)\), where \(F_n\) and \(L_n\) are the \(n\)th Fibonacci and Lucas numbers, respectively. Finally, they obtain several limit relations involving \(S(n)\) and its various composites with some arithmetic functions.