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.

• 2,
• 4,
• 8,
• 15,
• 26,
• 42,
• 64,
• ...

A positive integer greater than 1 that is not prime is called composite.

Composite numbers are opposite to prime numbers.

• ...,
• 10,
• 12,
• 14,
• 15,
• 16,
• 18,
• 20,
• ...

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.

• ...,
• 11,
• 13,
• 14,
• 15,
• 16,
• 17,
• 19,
• ...

The number n is evil if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

• ...,
• 9,
• 10,
• 12,
• 15,
• 17,
• 18,
• 20,
• ...

To build the lucky number sequence, start with natural numbers. Delete every second number, leaving 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, ... . The second number remaining is 3, so delete every third number, leaving 1, 3, 7, 9, 13, 15, 19, 21, ... . The next number remaining is 7, so delete every 7th number, leaving 1, 3, 7, 9, 13, 15, 21, ... . The next number remaining is 9, so delete every ninth number, etc.

Those numbers were lucky they weren't crossed out.

• ...,
• 7,
• 9,
• 13,
• 15,
• 21,
• 25,
• 31,
• ...

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.

• ...,
• 9,
• 11,
• 13,
• 15,
• 17,
• 19,
• 21,
• ...

A number is said to be square-free if its prime decomposition contains no repeated factors.

• ...,
• 11,
• 13,
• 14,
• 15,
• 17,
• 19,
• 21,
• ...

If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a triangle number.

Compare to square, pentagonal and tetrahedral numbers.

• ...,
• 3,
• 6,
• 10,
• 15,
• 21,
• 28,
• 36,
• ...