Journal of Integer Sequences, Vol. 4 (2001), Article 01.2.2

The gcd-sum function

Kevin A. Broughan

University of Waikato
Hamilton, New Zealand

Email address: kab@waikato.ac.nz

Abstract: The gcd-sum is an arithmetic function defined as the sum of the gcd's of the first n integers with n: g(n) = sum_i=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.

(Concerned with sequence A018804.)

Received April 2, 2001; published in Journal of Integer Sequences, Oct. 25, 2001.