Broughan, Kevin A.2009-02-172009-02-172001Broughan, K.A. (2001). The gcd-sum function. Journal of Integer Sequences, 4, Article 01.2.2.https://hdl.handle.net/10289/2024The gcd-sum is an arithmetic function defined as the sum of the gcd's of the first n integers with n: g(n) = sumi=1..n (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.application/pdfenThis article has been published in Journal of Integer Sequences. Copyright © 2001 Kevin A. Broughan.mathematicsJournal Article