Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Unique Properties of 216
- 216 is the smallest untouchable number which is also a cube
- Plato's number: Plato alludes to the fact that 216 is equal to 63, where 6 is one of the numbers representing marriage since it is the product of the female 2 and the male 3. Plato was also aware of the fact the the sum of the cubes of the 3-4-5 Pythagorean triple is equal to 216
- Two hundred sixteen 216 = 23*33 = 63 = 33 + 43 + 53, making it the smallest cube that's also the sum of three cubes
- 216 is the the number of colors in the Netscape Web-safe color palette
- 216 is the smallest magic product of a 3 by 3 multiplicative magic square
- 216 is the smallest abundant cube
- 216 is the smallest cube that is also a sum of several consecutive cubes: 216 = 27+64+125
Rare Properties of 216
The number n is a cube if it is the cube of an integer.
Common Properties of 216
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
A number is even if it is divisible by 2.
Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
The untouchable numbers are those that are not the sum of the proper divisors of any number.