n n
Σ (x, - 12) = -10 and Σ (x, - 3) = 62
i=1 i=1
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Let σ*(n) and φ*(n) be the unitary analogues of σ(n) and φ(n) respectively. It is known that E(x) = ∑n ≤ x σ*(n) - (π2x 2/12ζ(3)) = O(x log2 x) and F(x) = ∑n ≤ x φ*(n) - 1/2α x2 = O(x log2 x), where α is a positive constant. In this paper we improve the order estimates of E(x) and F(x) to E(x) = O(x log5/3 x) and F(x) = O(x log5/3 x(log log x)4/3).
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