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Exact and Asymptotic Evaluation of the Number of Distinct Primitive Cuboids
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Werner Hürlimann

Swiss Mathematical Society

Feldstrasse 145

CH-8004 Zürich

Switzerland

**Abstract:**

We express
the number of distinct primitive cuboids with given odd diagonal
in terms of the twisted Euler function with alternating
Dirichlet character of period four, and two counting formulas for binary
sums of squares. Based on the asymptotic behaviour of the sums of these
formulas, we derive
an approximation formula for the cumulative number of
primitive cuboids.

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(Concerned with sequences
A006752
A020882.)

Received August 1 2014; revised versions received August 6 2014;
January 12 2015; January 14 2015.
Published in *Journal of Integer
Sequences*, January 25 2015.

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