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 1430
- 1430 is the smallest Catalan number that is a product of four distinct primes: 1430 = 2*5*11*13 (submitted by Massimo Kofler)
Rare Properties of 1430
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.
Common Properties of 1430
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.
A number is said to be square-free if its prime decomposition contains no repeated factors.