# 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 253

- 253 is the smallest non-trivial triangular star number
- 253 is the smallest number n such that n
^{2} can be split into two nonzero squares (perhaps with leading zeros) in two different ways (253^{2} = 64009, and can be split as 64 and 009 or as 6400 and 9)

## Common Properties of 253

A positive integer greater than 1 that is not prime is called *composite*.

Composite numbers are opposite to prime numbers.

The number n is *deficient* if the sum of all its positive divisors except itself is less than n.

Compare with perfect and abundant numbers.

A number is *odd* if it is not divisible by 2.

Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.

The number n is *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.

A number is said to be *square-free* if its prime decomposition contains no repeated factors.

If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a *triangle* number.

Compare to square, pentagonal and tetrahedral numbers.

The next *Ulam* number is uniquely the sum of two earlier distinct Ulam numbers.