Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.5

Exact and Asymptotic Evaluation of the Number of Distinct Primitive Cuboids

Werner Hürlimann
Swiss Mathematical Society
Feldstrasse 145
CH-8004 Zürich


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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