(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Pentagonal numbers are of the form n(3n - 1)/2.
Pentagonal numbers are to pentagons what triangular numbers are to triangles and square numbers are to squares.
The number n is called a weird number if it is abundant but is not the sum of any subset of its proper factors.
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime 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.