\ Problem:
\ 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?
\ They don't count 0^1 (0 is not deemed to be positive)

\ Solution:
\ 10^n produces a n+1-digit integer, so we need only look at bases 0-9.

: n-digits { n -- n2 }
    \ number of n-th powers with n digits
    \ for n=1, it does not count 0 and 1 (I correct for the 1 below)
    \ this works by just seeing what the lowest x is that fits in
    \ 10^(n-1), and then rounding x up to an integer
    n 1- 0 d>f n 0 d>f f/ falog f>d drop 9 swap - ;

: solve ( -- )
    1 1 begin ( n sum ) 
        over n-digits dup 0> while
            + swap 1+ swap repeat
    drop nip ;

solve . cr