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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