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A study of the Dedekind psi function concludes that its extreme values aresupported on the subset of primorial integers N_k = 2*3***p_k, where p_k is thekth prime. In particular, the inequality psi(N_k) > cloglogN_k, c > 0 constant,holds for all large primorial integers.

Squarefree Integers And Extreme Values Of Some Arithmetic Functions