A "weird number" is a number that is abundant (i.e., the sum of proper divisors is greater than the number) without being pseudoperfect (i.e., no subset of the proper divisors sums to the number itself). The pseudoperfect part of the definition means that finding weird numbers is a case of the subset sum problem. Since prime numbers are deficient, prime numbers are not weird. Similarly, since multiples of 6 are pseudoperfect, no weird number is a multiple of 6.

abundant number | pseudoperfect number | Schnirelmann density | subset sum problem