A natural number N is such that it can be expressed as N = p + q + r, where p, q and r are distinct factors of N. How many numbers below 50 have this property?

We need numbers N < 50 expressible as a sum of three distinct factors of N. The classic example is N = 6 = 1+2+3. More generally, multiples of 6 work: N = 6k can be written as k + 2k + 3k where k, 2k, 3k are all factors of 6k. So multiples of 6 below 50 are 6, 12, 18, 24, 30, 36, 42, 48 — that gives 8 numbers. Each of these can be expressed as N/6 + N/3 + N/2 = N. Hence 8 numbers below 50 have this property.