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.

• ...,
• 734,
• 735,
• 737,
• 739,
• 741,
• 742,
• 743,
• ...

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

Guess what odious numbers are.

• ...,
• 732,
• 735,
• 736,
• 739,
• 741,
• 742,
• 745,
• ...

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.

• ...,
• 709,
• 716,
• 736,
• 739,
• 748,
• 761,
• 763,
• ...

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.

• ...,
• 727,
• 729,
• 735,
• 739,
• 741,
• 745,
• 769,
• ...

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.

• ...,
• 733,
• 735,
• 737,
• 739,
• 741,
• 743,
• 745,
• ...

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.

• ...,
• 719,
• 727,
• 733,
• 739,
• 743,
• 751,
• 757,
• ...

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

• ...,
• 733,
• 734,
• 737,
• 739,
• 741,
• 742,
• 743,
• ...

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

• ...,
• 722,
• 732,
• 734,
• 739,
• 751,
• 781,
• 783,
• ...