What is is 24 and 19 weird?

Are 24 and 19 Weird Numbers?

Whether a number is considered "weird" is a concept from number theory. A weird number is a positive integer that is abundant (the sum of its proper divisors is greater than the number itself) but is not a semiperfect number (it cannot be written as the sum of some or all of its proper divisors).

Let's analyze 24 and 19:

• 24: The proper divisors of 24 are 1, 2, 3, 4, 6, 8, and 12.

  • Their sum is 1 + 2 + 3 + 4 + 6 + 8 + 12 = 36. Since 36 > 24, 24 is an abundant number.
  • Now, let's see if 24 is semiperfect. Can we find a subset of its proper divisors that sum to 24? Yes: 12 + 8 + 4 = 24. Therefore, 24 is a semiperfect number.
  • Since 24 is abundant but also semiperfect, it is not a weird number.

• 19: The proper divisors of 19 are only 1 (because 19 is a prime number).

  • The sum of its proper divisors is 1. Since 1 < 19, 19 is not an abundant number. Therefore, 19 cannot be a weird number.