# 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 532

- 532 is the smallest even number differing by a composite number from both of its prime neighbors (submitted by Alexey Radul)
- 532 is the smallest number n such that the sum of nonprime divisors of n minus the sum of prime divisors of n equals n
- 532 is the smallest number n such that σ(n)-σ(n+1) equals n
- 532 is the smallest n such that both n and n+2 are nontotients and noncototients

## Common Properties of 532

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.

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