[math-fun] Sum of reciprocals of 8877690 integers with distinct digits

Problem E2533 in the American Mathematical Monthly (1975 or 1976) says there are 8877690 integers that have distinct digits. The problem is to estimate the sum of their reciprocals. I thought I read someplace that someone had computed the exact sum. Does anyone know how big the numerator and denominator are? And, by the way, what is the approximate sum? Bob Baillie