Project Euler Problem 63

http://projecteuler.net/problem=63

Problem 63

13 February 2004

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?

Answer:

49

* Racket

#lang racket
(define (digits n)
  (add1 (floor (/ (log n) (log 10)))))

(define sum 0)
(define d 1)
(for* ([n (in-range 1 10)]
       [d (in-range 1 22)])
  (when (= d (digits (expt n d)))
    (set! sum (add1 sum))))

(print sum)