# 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 272

- 272 is the smallest nontrivial palindrome that is a product of two consecutive numbers
- 272 is the smallest palindrome divisible by a fourth power

## Rare Properties of 272

The number is called *pronic* if it is the product of two consecutive numbers.

They are twice triangular numbers.

## Common Properties of 272

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.

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.

A *palindrome* is a number that reads the same forward or backward.

The number n is *practical* if all numbers strictly less than n are sums of distinct divisors of n.

*Undulating* numbers are numbers of the form abababab... in base 10.

This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.