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.

• ...,
• 8715,
• 8716,
• 8717,
• 8719,
• 8721,
• 8722,
• 8723,
• ...

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

Guess what odious numbers are.

• ...,
• 8713,
• 8714,
• 8716,
• 8719,
• 8721,
• 8722,
• 8724,
• ...

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.

• ...,
• 8661,
• 8673,
• 8683,
• 8719,
• 8757,
• 8769,
• 8773,
• ...

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.

• ...,
• 8713,
• 8715,
• 8717,
• 8719,
• 8721,
• 8723,
• 8725,
• ...

A prime is a positive integer greater than 1 that is divisible by no positive integers other than 1 and itself.

Prime numbers are opposite to composite numbers.

• ...,
• 8699,
• 8707,
• 8713,
• 8719,
• 8731,
• 8737,
• 8741,
• ...

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

• ...,
• 8715,
• 8717,
• 8718,
• 8719,
• 8723,
• 8726,
• 8727,
• ...