Powerful digit counts

Show HTML problem contentShow HTML problem content  Published on Friday, 13th February 2004, 06:00 pm; Solved by 41556;
Difficulty rating: 5%

Problem 63

The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number, 134217728=89, is a ninth power.

How many n-digit positive integers exist which are also an nth power?