Definition 5 (Möbius Function). The Möbius u-function is defined for all n EN by 1 if n = 1; H(n) = if p2 | n for some prime p; -1)* if n = p1· · ·Pt is the product of t > 1 distinct primes. Lemma 6. For all n E N, Eh(d) = >h(), whenever h is an arithmetic function. d|n d|n Theorem 7 (Möbius Inversion Formula). Let f and g be arithmetic functions. Then f (n) = g(d), for all n E N (3) d|n if and only if g(n) = Ef(G)u(d) =d)), for all n e N. (4) d|n d|n

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