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 866
- 866 is the smallest number n such that the sum of the proper divisors of n2, excluding 1, is a square
- 866 is the smallest number that together with the next 4 numbers have the property that they are not divisible by any of their nonzero digits
Common Properties of 866
The number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal).
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.
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 odious if it has an odd number of 1's in its binary expansion.
Guess what evil 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.