# 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 546

- 546 is the smallest number which is the sum of its proper divisors containing the digit 2 (2 + 21 + 26 + 42 + 182 + 273 = 546)

## Common Properties of 546

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.

A number is said to be *square-free* if its prime decomposition contains no repeated factors.

The next *Ulam* number is uniquely the sum of two earlier distinct Ulam numbers.