Weird number

The number 12, for example, is abundant but not weird, because the proper divisors of 12 are 1, 2, 3, 4, and 6, which sum to 16; but 2 + 4 + 6 = 12.

In fact, the set of weird numbers has positive asymptotic density.

are primitive, but the existence of infinitely many k and Q which yield a prime R is not guaranteed.

It is conjectured that there exist infinitely many primitive weird numbers, and Melfi has shown that the infinitude of primitive weird numbers is a consequence of Cramér's conjecture.

[7] Primitive weird numbers with as many as 16 prime factors and 14712 digits have been found.