# 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 954

- 954 is the smallest number n such that if you subtract its reverse from it you would get a natural number with the same digits as n: 954 - 459 = 495
- 954 is the smallest number n such that σ(n) = σ(n+1)+σ(n-1)
- 954 is the largest 3-digit number n, such that the sum of the digit splits of n is equal to the product of the digits of n: (9 + 54) + (95 + 4) + (9 + 5 + 4) = 9 * 5 * 4

## Common Properties of 954

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 *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.