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
- Soma cube has 240 solutions
- There 240 mountain numbers (digits go up then down) with 3 digits
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.