The gcd-sum function
Broughan, K.A. (2001). The gcd-sum function. Journal of Integer Sequences, 4, Article 01.2.2.
Permanent Research Commons link: http://hdl.handle.net/10289/2024
The 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.
University of Waterloo
This article has been published in Journal of Integer Sequences. Copyright © 2001 Kevin A. Broughan.