# 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 4150

- 4150 is the smallest number except 1 which is the sum of the fifth powers of its digits: 4150 = 4
^{5} + 1^{5} + 5^{5} + 0^{5}
- 4150 is the smallest number which equals to the sum of a fixed power of their digits where that power is not equal to the length of the number

## Common Properties of 4150

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.

The next *Ulam* number is uniquely the sum of two earlier distinct Ulam numbers.