The number n is a square if it is the square of an integer.

• ...,
• 256,
• 289,
• 324,
• 361,
• 400,
• 441,
• 484,
• ...

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

• ...,
• 287,
• 312,
• 355,
• 361,
• 366,
• 382,
• 384,
• ...

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

Composite numbers are opposite to prime numbers.

• ...,
• 357,
• 358,
• 360,
• 361,
• 362,
• 363,
• 364,
• ...

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.

• ...,
• 357,
• 358,
• 359,
• 361,
• 362,
• 363,
• 365,
• ...

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.

• ...,
• 339,
• 349,
• 357,
• 361,
• 367,
• 385,
• 391,
• ...

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.

• ...,
• 355,
• 357,
• 359,
• 361,
• 363,
• 365,
• 367,
• ...

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

Guess what evil numbers are.

• ...,
• 355,
• 357,
• 358,
• 361,
• 362,
• 364,
• 367,
• ...

An integer n is powerful if for every prime p dividing n, p² also divides n.

How much power? They all can be written as a² b³.

• ...,
• 289,
• 324,
• 343,
• 361,
• 392,
• 400,
• 432,
• ...