What is is 18 and 23 weird?

Numbers 18 and 23 are not typically considered "weird" in a mathematical sense. The concept of a "weird number" has a specific definition in number theory.

  • Weird Numbers: In mathematics, a weird number is a number that is abundant (the sum of its proper divisors is greater than the number itself) but not a semiperfect number (no subset of its proper divisors sums to the number itself). The smallest weird number is 70.

  • 18: The proper divisors of 18 are 1, 2, 3, 6, and 9. Their sum is 1 + 2 + 3 + 6 + 9 = 21. Since 21 > 18, 18 is an abundant number. However, 1 + 2 + 3 + 6 + 9 = 18, hence 18 is a semiperfect number and not a weird number.

  • 23: 23 is a prime number. Prime numbers only have 1 and themselves as divisors. The only proper divisor of 23 is 1. Since 1 < 23, 23 is a deficient number (the sum of its proper divisors is less than the number itself), and therefore, definitely not a weird number (which must be abundant).