5kyu_What'sAPerfectPowerAnyway.js

// 5kyu - What's a Perfect Power anyway?

// Description:

// A perfect power is a classification of positive integers:

// In mathematics, a perfect power is a positive integer that can be expressed as an 
// integer power of another positive integer. More formally, n is a perfect power if 
// there exist natural numbers m > 1, and k > 1 such that mk = n.
// Your task is to check wheter a given integer is a perfect power. If it is a perfect 
// power, return a pair m and k with mk = n as a proof. Otherwise return Nothing, Nil, 
// null, None or your language's equivalent.

// Note: For a perfect power, there might be several pairs. For example 81 = 3^4 = 9^2, so (3,4) and (9,2) are valid solutions. However, the tests take care of this, so if a number is a perfect power, return any pair that proves it.

// Examples

// Test.describe("perfect powers", function(){
//   Test.it("should work for some examples",function(){
//     Test.assertSimilar(isPP(4), [2,2], "4 = 2^2");
//     Test.assertSimilar(isPP(9), [3,2], "9 = 3^2");
//     Test.assertEquals( isPP(5), null, "5 isn't a perfect number");
//   });
// });

let isPP = function(n) {
  let k = Math.log(n)/Math.LN2;
  if(Math.pow(n, 1/2) % 1 === 0) { return [Math.pow(n, 1/2), 2]; }
  for(let i = 2; i <= ~~k; i+=1){
    let x = Math.round(Math.pow(n, 1/i));
    if(Math.pow(x, i) === n) {
      return [x, i]    
    }
  }
  return null;
}