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.

• ...,
• 26,
• 42,
• 64,
• 93,
• 130,
• 176,
• 232,
• ...

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

Composite numbers are opposite to prime numbers.

• ...,
• 90,
• 91,
• 92,
• 93,
• 94,
• 95,
• 96,
• ...

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.

• ...,
• 89,
• 91,
• 92,
• 93,
• 94,
• 95,
• 97,
• ...

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.

• ...,
• 75,
• 79,
• 87,
• 93,
• 99,
• 105,
• 111,
• ...

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.

• ...,
• 87,
• 89,
• 91,
• 93,
• 95,
• 97,
• 99,
• ...

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

Guess what evil numbers are.

• ...,
• 87,
• 88,
• 91,
• 93,
• 94,
• 97,
• 98,
• ...

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

• ...,
• 87,
• 89,
• 91,
• 93,
• 94,
• 95,
• 97,
• ...