# 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 364

- 364 is the sum of squares of the first prime quadruplet (364 = 5
^{2} + 7^{2} + 11^{2} + 13^^{2})
- The first two digits of 364 are the product of the first two primes to the power of the first prime, and the last two digits are the first prime to the product of the first two primes (36 = (2*3)
^{2}, and 64 = 2^{2*3})
- 364 is the total number of gifts received in the song "The Twelve Days of Christmas"

## Rare Properties of 364

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 364

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

Guess what evil numbers are.

The number n is *practical* if all numbers strictly less than n are sums of distinct divisors of n.