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 441
- 441 is the sum of the first 6 cubes
- 441 is the smallest square that can be written as a sum of 3 distinct nonzero squares in 3 or more ways
- 441 is the smallest power that is equal to a sum of first n primes plus 1
Rare Properties of 441
The number n is a square if it is the square of an integer.
Common Properties of 441
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.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.