# 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 1260

- 1260 is the smallest number n such that φ(n+1) = 4φ(n)

## Rare Properties of 1260

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

They are twice triangular numbers.

The number n is called a *vampire* number if there exists a factorization of n using n's digits (counting multiplicity).

## Common Properties of 1260

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.

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