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.

• ...,
• 44,
• 45,
• 46,
• 47,
• 49,
• 50,
• 51,
• ...

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.

• ...,
• 41,
• 43,
• 45,
• 47,
• 49,
• 51,
• 53,
• ...

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

Guess what evil numbers are.

• ...,
• 41,
• 42,
• 44,
• 47,
• 49,
• 50,
• 52,
• ...

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.

• ...,
• 37,
• 41,
• 43,
• 47,
• 53,
• 59,
• 61,
• ...

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

• ...,
• 42,
• 43,
• 46,
• 47,
• 51,
• 53,
• 55,
• ...

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

• ...,
• 28,
• 36,
• 38,
• 47,
• 48,
• 53,
• 57,
• ...