# 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 286

- 286 is the smallest even pseudoprime to base 3
- 286 is the smallest perimeter of a primitive Pythagorean triangle no side of which is squarefree (the sides are 44, 125, and 117)

## Rare Properties of 286

A *tetrahedral* number is the number of balls you can put in a triangular pyramid.

This is the space generalization of triangular and square numbers.

## Common Properties of 286

The number n is called an *apocalyptic power* if 2^{n} contains the consecutive digits 666 (in decimal).

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 *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 *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.