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 225
- 225 is the smallest square that starts with 2 identical digits
- 225 is the smallest octagonal square (except trivial 1)
- 225 is the smallest square whose external digits form a square and whose internal digits form a prime
- 225 is the only three-digit square with all prime digits
- 225 is the smallest square that remain a square if prefixed with 1
- 225 is the smallest square which is pandigital is some base: 225 is 3201 is base 4
- 225 is the smallest odd power that is not prime power
- 225 is the smallest sum of a set of odd numbers that contain every digit once
Rare Properties of 225
The number n is a square if it is the square of an integer.
Common Properties of 225
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
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.
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 odd if it is not divisible by 2.
Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.