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 240
- 240 is the smallest number with 20 divisors
- The maximum number of divisors for any integer less than a million is 240
- 240 is the smallest magic constant of a pan-diagonal magic square which consist of distinct prime numbers (this square is of order 4)
- The most special root system E8 has 240 root vectors
- 240 is the largest side of the smallest Euler brick
- Soma cube has 240 solutions
- There 240 mountain numbers (digits go up then down) with 3 digits
- 240 is the number of ways to color a cube in at most 4 colors (up to rotations)
Rare Properties of 240
The number is called pronic if it is the product of two consecutive numbers.
They are twice triangular numbers.
Common Properties of 240
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.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.