# 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 701

- 701 can be expressed as 1
^{0}+2^{1}+3^{2}+4^{3}+5^{4} = 1+2+9+64+625
- 701 is the smallest prime of the form 100p + 1, where p is prime
- 701 is the smallest prime whose square (491401) contains all the square digits (0,1,4,9) and only them

## Common Properties of 701

The number n is *deficient* if the sum of all its positive divisors except itself is less than n.

Compare with perfect and abundant numbers.

A number is *odd* if it is not divisible by 2.

Numbers that are not odd are even. 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.

A *prime* is a positive integer greater than 1 that is divisible by no positive integers other than 1 and itself.

Prime numbers are opposite to composite numbers.

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