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The gcd-sum function

The gcd-sum is an arithmetic function defined as the sum of the gcd’s of the first n integers with n : g(n) = P n=1 (i,n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of partial sums of the Dirichlet series at real values are derived, including estimates for error terms.