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 and 1/2+1/2=1, and 11=2+3+6 and 1/2+1/3+1/6=1. But 2, 3, and 5 are unlucky. How many unlucky positive integers are there?

There are an unlucky number of unlucky numbers. There are 13 unlucky numbers! (2, 3, 5, 6, 7, 8, 12, 13, 14, 15, 19, 21, 23)

Posted by Math Man on 2011-04-09 16:54:46