A Dedekind Psi Function Inequality
  This note shows that the Dedekind psi function achieves its extreme values on the subset of primorial integers N_k = 2*3*5*...*p_k, where p_k is the kth prime. In particular, the inequality psi(N_k) > cloglog N_k, where c = 1.08... is a universal constant, holds for all large primorial integers N_k = 2*3*5*...*p_k unconditionally. 
N. A. Carella
math.NT