What is is 19 and 26 weird?

"Weird numbers" are a type of number with a specific mathematical property. A weird number is a natural number that is abundant but not semiperfect. This means:

1. It is abundant: The sum of its proper divisors (excluding the number itself) is greater than the number.
2. It is not semiperfect: No subset of its proper divisors sums to the number itself.

Given this definition, let's analyze the numbers 19 and 26:

• 19: The proper divisors of 19 are just 1 because 19 is a prime number. The sum of its proper divisors is 1, which is not greater than 19. Therefore, 19 is not abundant and cannot be a weird number.

• 26: The proper divisors of 26 are 1, 2, and 13. The sum of these divisors is 1 + 2 + 13 = 16, which is less than 26, so 26 is not abundant and thus cannot be a weird number.

In conclusion, neither 19 nor 26 are weird numbers according to the mathematical definition.