We call an integer lucky if it is a sum of positive integers (not necessarily distinct) whose reciprocals sum to 1. For example, 4 and 11 are lucky: 4=2+2, 1/2 + 1/2 = 1, and 11=2+3+6, 1/2 + 1/3 + 1/6=1. However, 2, 3, and 5 are unlucky. Find all unlucky numbers.