The number n is called an aspiring number if its aliquot sequence terminates in a perfect number, and it is not a perfect number itself.

• ...,
• 6099,
• 6123,
• 6145,
• 6663,
• 6672,
• 7025,
• 7149,
• ...

The number n is called an apocalyptic power if 2ⁿ contains the consecutive digits 666 (in decimal).

• ...,
• 6659,
• 6661,
• 6662,
• 6663,
• 6664,
• 6666,
• 6667,
• ...

A positive integer greater than 1 that is not prime is called composite.

Composite numbers are opposite to prime numbers.

• ...,
• 6658,
• 6660,
• 6662,
• 6663,
• 6664,
• 6665,
• 6666,
• ...

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.

• ...,
• 6659,
• 6661,
• 6662,
• 6663,
• 6665,
• 6667,
• 6668,
• ...

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

Guess what odious numbers are.

• ...,
• 6657,
• 6658,
• 6660,
• 6663,
• 6664,
• 6667,
• 6669,
• ...

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.

• ...,
• 6625,
• 6631,
• 6661,
• 6663,
• 6667,
• 6669,
• 6679,
• ...

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.

• ...,
• 6657,
• 6659,
• 6661,
• 6663,
• 6665,
• 6667,
• 6669,
• ...

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

• ...,
• 6659,
• 6661,
• 6662,
• 6663,
• 6665,
• 6666,
• 6667,
• ...