Polynomial analogue of the Smarandache function

A proof of Sondow's conjecture on the Smarandache function

“…In Case (i) there are at most 12 possibilities of n by considering K(n) = P (n) ≤ 5 (that is, 1, 2, 3,5,6,10,15,20,30,40,60,120). For any integer n in Case (ii), using Lemma 2.2 we have e P (n) e ).…”

“…It is also sometimes called the Smarandache function following Smarandache's rediscovery in 1980; see [9]. In addition, the polynomial analogue of the Kempner function has been applied in [4,5] and studied detailedly in [6].…”