# 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 407

- 407 is the largest number that is the sum of the cubes of its digits

## Rare Properties of 407

A k-digit number n is called *narcissistic* if it is equal to the sum of k-th powers of its digits. They are also called *Plus Perfect* numbers.

## Common Properties of 407

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.

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 *odd* if it is not divisible by 2.

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

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