# 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 245

- 245 is the smallest positive integer whose square is the sum of 50 consecutive squares (the square of 245 is the sum of squares from 7 to 56 inclusive)
- 245 is the largest integer that is not the sum of 5 distinct nonzero squares

## Common Properties of 245

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.

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

Guess what odious numbers are.

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.