# 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 46

- 46 is the number of human chromosomes
- 46 is the least even number 2k such that the sum of the first k primes is divisible by 2k
- The Tutte graph has 46 vertices
- 46 is the largest even integer for which there is no pair of abundant numbers that add up to it

## Common Properties of 46

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 *evil* if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

The n-th *lazy caterer* number is the maximum number of pieces a (circular) pizza can be cut into with n (straight-line) cuts.

Unlike the situation with cake, everybody gets the toppings.

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