A Proof of Sondow’s Conjecture on the Smarandache Function
A Proof of Sondow’s Conjecture on the Smarandache Function
The Smarandache function of a positive integer n, denoted by S(n), is defined to be the smallest positive integer j such that n divides the factorial j!. In this note, we prove that for any fixed number k > 1, the inequality nk<S(n)! holds for almost all positive integers n. …