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) = 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.


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(Concerned with sequence A018804.)


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


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