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.

• ...,
• 1034,
• 1035,
• 1037,
• 1039,
• 1041,
• 1042,
• 1043,
• ...

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.

• ...,
• 1029,
• 1030,
• 1033,
• 1039,
• 1067,
• 1076,
• 1088,
• ...

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.

• ...,
• 1021,
• 1023,
• 1029,
• 1039,
• 1041,
• 1053,
• 1057,
• ...

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.

• ...,
• 1033,
• 1035,
• 1037,
• 1039,
• 1041,
• 1043,
• 1045,
• ...

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

Guess what evil numbers are.

• ...,
• 1033,
• 1034,
• 1036,
• 1039,
• 1041,
• 1042,
• 1044,
• ...

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.

• ...,
• 1021,
• 1031,
• 1033,
• 1039,
• 1049,
• 1051,
• 1061,
• ...

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

• ...,
• 1034,
• 1037,
• 1038,
• 1039,
• 1041,
• 1042,
• 1043,
• ...