What is is 19 and 24 weird?

In the context of number theory, the term "weird number" refers to a specific kind of integer with unique properties. A weird number is a natural number that is abundant but not semiperfect.

Here's what these terms mean:

1. Abundant Number: A number is considered abundant if the sum of its proper divisors (excluding the number itself) is greater than the number. For example, the number 12 is abundant because its proper divisors (1, 2, 3, 4, 6) sum to 16, which is greater than 12.

2. Semiperfect Number (or Pseudoperfect Number): A number is semiperfect if it is equal to the sum of some (or all) of its proper divisors.

A weird number is abundant but not semiperfect. This means that while the sum of its proper divisors is greater than the number itself, no subset of those divisors adds up exactly to the number.

Now, let's look at the numbers you mentioned:

• 19: The proper divisors of 19 are just 1, as 19 is a prime number. Since 1 is less than 19, it is neither abundant nor semiperfect. Therefore, 19 is not a weird number.

• 24: The proper divisors of 24 are 1, 2, 3, 4, 6, 8, and 12. The sum is 36, which is greater than 24, making 24 abundant. However, 24 is not a weird number because it is semiperfect; for example, 12 + 8 + 4 = 24.

In conclusion, neither 19 nor 24 are weird numbers.