1. PANORAMA OF ARITHMETIC FUNCTIONS 7 From (1.21) we derive by induction in k that Λk(n) 0 and Λk(n) is supported on positive integers having at most k distinct prime divisors. Moreover we get by (1.20) that (1.22) 0 Λk(n) (log n)k. Exercise. Prove the formula (1.23) Λk(mn) = 0 j k k j Λj(m)Λk−j(n). Exercise. Prove the formula (1.24) p 1 ps = 1 μ(n) n log ζ(ns), if s 1.
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