# 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 102

- 102 is the smallest number with three different digits
- 102 is the alphanumeric value of THOUSAND
- 102 is the smallest Ulam number which is a product of three distinct primes: 102 = 2*3*17 (submitted by Massimo Kofler)
- 102 is the smallest number m such that m times the number consisting of m ones is one greater than a prime number

## Common Properties of 102

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.

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