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.

• ...,
• 987,
• 988,
• 989,
• 991,
• 993,
• 994,
• 995,
• ...

The n-th lazy caterer number is the maximum number of pieces a (circular) pizza can be cut into with n (straight-line) cuts.

Unlike the situation with cake, everybody gets the toppings.

• ...,
• 862,
• 904,
• 947,
• 991,
• 1036,
• 1082,
• 1129,
• ...

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.

• ...,
• 975,
• 979,
• 981,
• 991,
• 993,
• 997,
• 1009,
• ...

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.

• ...,
• 985,
• 987,
• 989,
• 991,
• 993,
• 995,
• 997,
• ...

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

Guess what evil numbers are.

• ...,
• 985,
• 986,
• 988,
• 991,
• 992,
• 995,
• 997,
• ...

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.

• ...,
• 971,
• 977,
• 983,
• 991,
• 997,
• 1009,
• 1013,
• ...

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

• ...,
• 986,
• 987,
• 989,
• 991,
• 993,
• 994,
• 995,
• ...

The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.

• ...,
• 949,
• 983,
• 986,
• 991,
• 1018,
• 1020,
• 1023,
• ...