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 57
- 57 is the smallest integer k such that k2 + 1 is divisible by a cube
- 57 is the number of ways to color a cube in at most 3 colors (up to rotations)
Common Properties of 57
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.
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.