What is is 17 and 21 weird?

Are 17 and 21 "weird"? This refers to the concept of weird numbers.

A weird number is a number that is abundant but not semiperfect.

• An abundant number is a number where the sum of its proper divisors (divisors excluding the number itself) is greater than the number.

• A semiperfect number is a number that can be expressed as the sum of some or all of its proper divisors.

17:

• The divisors of 17 are 1 and 17. Its proper divisors consist only of 1.
• The sum of the proper divisors of 17 is 1.
• Since 1 < 17, 17 is a deficient number, not an abundant number.
• Therefore, 17 is not a weird number.

21:

• The divisors of 21 are 1, 3, 7, and 21. Its proper divisors are 1, 3, and 7.
• The sum of the proper divisors of 21 is 1 + 3 + 7 = 11.
• Since 11 < 21, 21 is a deficient number, not an abundant number.
• Therefore, 21 is not a weird number.

Therefore, neither 17 nor 21 are weird numbers. The smallest weird number is 70.