Powerful digit counts
The \( 5 \)-digit number, \( 16807=7^5 \), is also a fifth power. Similarly, the \( 9 \)-digit number, \( 134217728=8^9 \), is a ninth power.
How many n-digit positive integers exist which are also an nth power?
The \( 5 \)-digit number, \( 16807=7^5 \), is also a fifth power. Similarly, the \( 9 \)-digit number, \( 134217728=8^9 \), is a ninth power.
How many n-digit positive integers exist which are also an nth power?