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.

• ...,
• 1089,
• 1090,
• 1091,
• 1093,
• 1094,
• 1095,
• 1096,
• ...

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

Guess what odious numbers are.

• ...,
• 1086,
• 1088,
• 1091,
• 1093,
• 1094,
• 1097,
• 1098,
• ...

One can take the sum of the squares of the digits of a number. Those numbers are happy for which iterating this operation eventually leads to 1.

• ...,
• 1088,
• 1090,
• 1092,
• 1093,
• 1112,
• 1114,
• 1115,
• ...

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.

• ...,
• 1053,
• 1057,
• 1087,
• 1093,
• 1095,
• 1101,
• 1105,
• ...

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.

• ...,
• 1087,
• 1089,
• 1091,
• 1093,
• 1095,
• 1097,
• 1099,
• ...

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.

• ...,
• 1069,
• 1087,
• 1091,
• 1093,
• 1097,
• 1103,
• 1109,
• ...

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

• ...,
• 1087,
• 1090,
• 1091,
• 1093,
• 1094,
• 1095,
• 1097,
• ...

A prime number is called a twin prime if there exists another prime number differing from it by 2.

• ...,
• 1061,
• 1063,
• 1091,
• 1093,
• 1151,
• 1153,
• 1229,
• ...