Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Rare Properties of 2626
The n-th cake number is the maximum number of pieces a (cylindrical) cake can be cut into with n (straight-plane) cuts.
Unfortunately, not everybody gets the frosting. If you cut pizza rather than cake, you get lazy caterer's numbers.
Common Properties of 2626
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 evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
A number is said to be square-free if its prime decomposition contains no repeated factors.
Undulating numbers are numbers of the form abababab... in base 10.
This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.