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 132
- 132 is the smallest composite number that uses exactly the same digits as its prime factors: 132 = 2 * 2 * 3 * 11
- 132 is the smallest number n such that n concatenated with itself gives the product of two numbers which differ by 1 (132132 = 363 * 364)
- If you take the sum of all the 2-digit numbers you can make from 132, you get 132: 12 + 13 + 21 + 23 + 31 + 32 = 132: 132 is the smallest number with this property
Rare Properties of 132
The n-th Catalan number is equal to (2n choose n)/(n+1) = (2n)!/(n!(n+1)!).
There are many ways Catalan numbers can be interpreted; there are some cool pictures here and the Wikipedia article is very good.
The number is called pronic if it is the product of two consecutive numbers.
They are twice triangular numbers.
Common Properties of 132
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.