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**The gcd-sum function**

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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.

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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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