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.

• ...,
• 417,
• 418,
• 419,
• 421,
• 422,
• 423,
• 424,
• ...

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.

• ...,
• 399,
• 409,
• 415,
• 421,
• 427,
• 429,
• 433,
• ...

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.

• ...,
• 415,
• 417,
• 419,
• 421,
• 423,
• 425,
• 427,
• ...

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

Guess what evil numbers are.

• ...,
• 415,
• 416,
• 419,
• 421,
• 422,
• 425,
• 426,
• ...

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.

• ...,
• 401,
• 409,
• 419,
• 421,
• 431,
• 433,
• 439,
• ...

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

• ...,
• 417,
• 418,
• 419,
• 421,
• 422,
• 426,
• 427,
• ...

A prime number is called a twin prime if there exists another prime number differing from it by 2.

• ...,
• 347,
• 349,
• 419,
• 421,
• 431,
• 433,
• 461,
• ...