# What are weird numbers?

**What are weird numbers?** To understand them, we must first begin with "abundant" numbers. Abundant numbers, also known as "excessive," are bigger than the sum of their proper divisors. 12, for instance, is the first (smallest) abundant number–the sum of its proper divisors, 1+2+3+4+6, is 16. 12, therefore, has an "abundance" of 4, the amount by which the sum of its divisors exceeds the number. There are many even abundant numbers, but we dont get to an odd one until the number 945.
Some abundant numbers are "semiperfect" or "pseudoperfect," meaning that they are equal to all or just some of their proper divisors. 12 is an imperfect abundant number because some of its divisors can be added together to form 12.
At last, we arrive at weird numbers. A number is weird if it is abundant but NOT semiperfect; in other words, the sum of its divisors is larger than the number itself, but no subset of divisor sums equal the number. Weird numbers are uncommon – the first few are 70, 836, 4,030, and 5,830.