432 Hz versus 440 Hz

I've been aware for a while about the the controversy surrounding the standard A note and whether it should be set to $440 \text{Hz}$ (as it now is) or changed to $432 \text{Hz}.$ I'm trying in this post to look at the mathematical properties of $432$.

• $432^2 = 186624$ is close to the speed of light as measured in miles per second. Wolfram Alpha gives a figure of $186282$ miles per second for the speed of light in a vacuum which is $99.82 \text{%}$ of $432^2$.
  
  
• It also turns out that the area of an equilateral triangle whose numerical area is equal to its perimeter is given by $12 \sqrt{3} = \sqrt{432}$.
  
  
• $432$ sits between the twin primes $431$ and $433$
  
  
• The factors of $432$ are $1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216 \text{ and } 432$. The sum of these divisors is $1240$.
  
  
• $432$ is a 3-smooth number, one that is of the form $2^i*3^j \text{ where }i,j>=0$ or to put it less mathematically it is a number that can be written as a power of two times a power of three, specifically $2^4×3^3$. Such numbers have been called harmonic numbers. Here are the harmonic numbers up to $1000$:
  
  

• $432$ is the sum of four consecutive primes: $103+107+109+113 = 432$
  
  
• $432$ is the sum of two positive cubes: $6^3+6^3=432$
  
  
• OEIS lists $2944$ entries for the number $432$