# 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 836

- 836 is the numerical equivalent of the word TEN on a touch-tone telephone
- 836 is the smallest number such that its square is a palindrome with an even number of digits
- 836 is the smallest weird untouchable number

## Rare Properties of 836

The number n is called a *weird* number if it is abundant but is not the sum of any subset of its proper factors.

## Common Properties of 836

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.

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.

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.

One can take the sum of the squares of the digits of a number. Those numbers are *happy* for which iterating this operation eventually leads to 1.

The *untouchable* numbers are those that are not the sum of the proper divisors of any number.