Other Applications
Heninger, Rains & Sloane (2005) show that, when n is a regular number and is divisible by 8, the generating function of an n-dimensional extremal even unimodular lattice is an nth power of a polynomial.
As with other classes of smooth numbers, regular numbers are important as problem sizes in computer programs for performing the fast Fourier transform, a technique for analyzing the dominant frequencies of signals in time-varying data. For instance, the method of Temperton (1992) requires that the transform length be a regular number.
Book VIII of Plato's Republic involves an allegory of marriage centered around the highly regular number 604 = 12,960,000 and its divisors. Later scholars have invoked both Babylonian mathematics and music theory in an attempt to explain this passage.
Read more about this topic: Regular Number