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

• ...,
• 529,
• 539,
• 540,
• 541,
• 564,
• 578,
• 580,
• ...

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.

• ...,
• 537,
• 538,
• 539,
• 541,
• 542,
• 543,
• 545,
• ...

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.

• ...,
• 529,
• 535,
• 537,
• 541,
• 553,
• 559,
• 577,
• ...

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.

• ...,
• 535,
• 537,
• 539,
• 541,
• 543,
• 545,
• 547,
• ...

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

Guess what evil numbers are.

• ...,
• 535,
• 536,
• 539,
• 541,
• 542,
• 545,
• 546,
• ...

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.

• ...,
• 509,
• 521,
• 523,
• 541,
• 547,
• 557,
• 563,
• ...

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

• ...,
• 535,
• 537,
• 538,
• 541,
• 542,
• 543,
• 545,
• ...