problem 63 // project euler

Powerful digit counts

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 n^th power?

幂次与位数

五位数16807=7⁵同时也是一个五次幂。同样的，九位数134217728=8⁹同时也是九次幂。

有多少个n位正整数同时也是n次幂？