# 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 354

- 354 is the smallest number whose first two digits are distinct primes and whose third digit is the arithmetic mean of the first two
- 354 is the sum of the first 4 non-negative 4
^{th} powers
- 354 is the sum of the absolute value of the coefficients of Conway's polynomial in the Look-and-See sequence

## Common Properties of 354

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