The number n is a square if it is the square of an integer.

• ...,
• 100,
• 121,
• 144,
• 169,
• 196,
• 225,
• 256,
• ...

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

Composite numbers are opposite to prime numbers.

• ...,
• 165,
• 166,
• 168,
• 169,
• 170,
• 171,
• 172,
• ...

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.

• ...,
• 165,
• 166,
• 167,
• 169,
• 170,
• 171,
• 172,
• ...

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

Guess what odious numbers are.

• ...,
• 163,
• 165,
• 166,
• 169,
• 170,
• 172,
• 175,
• ...

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.

• ...,
• 151,
• 159,
• 163,
• 169,
• 171,
• 189,
• 193,
• ...

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.

• ...,
• 163,
• 165,
• 167,
• 169,
• 171,
• 173,
• 175,
• ...

An integer n is powerful if for every prime p dividing n, p² also divides n.

How much power? They all can be written as a² b³.

• ...,
• 125,
• 128,
• 144,
• 169,
• 196,
• 200,
• 216,
• ...