The positive integers 216 and 
appear in an obscure passage in Plato's The Republic.
In this passage, Plato alludes to the fact that 216 is equal to 
, where 6 is one of the numbers representing marriage since
it is the product to the female 2 and the male 3. Plato was also aware of the fact
the sum of the cubes of the 3-4-5 Pythagorean triple
is equal to 
(Livio 2002, p. 66).
In Laws, Plato suggests that 
is the optimal number of citizens in a state because
1. It is the product of 12, 20, and 21.
2. The 12th part of it can still be divided by 12.
3. It has 59 proper divisors, including all numbers for 1 to 12 except 11, and 5038--which is very close to 5040--is divisible by 11
(Livio 2002, p. 65).
