029.js

/*
Problem 29: Distinct powers
Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

22=4, 23=8, 24=16, 25=32

32=9, 33=27, 34=81, 35=243

42=16, 43=64, 44=256, 45=1024

52=25, 53=125, 54=625, 55=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ n and 2 ≤ b ≤ n?
*/
const distinctPowers = n => {
  let distinct = new Set();
  for (let x = 2; x <= n; x++)
    for (let y = 2; y <= n; y++)
      distinct.add(x ** y)
  return distinct.size;
}

console.log(distinctPowers(30));