# 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 168

- 168 is the number of hours in a week
- 168 is the size of the smallest non-cyclic simple group which is not an alternating group
- 168 is the number of primes less than 1000
- 168 is the total number of spots on a set of dominoes (submitted by Ken Knowlton)
- 165 is the smallest number with more than one nonzero digit whose cubed digits sum to a cube (1
^{3} + 6^{3} + 8^{3} = 729 = 9^{3})
- 168 is the smallest integer areas of an integer-sided triangle such that the length of its circumradius is a square

## Common Properties of 168

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.