curriculum/challenges/english/blocks/project-euler-problems-1-to-100/5900f3891000cf542c50fe9c.md
Consider all integer combinations of $a^b$ for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
<div style='padding-left: 4em;'> 2<sup>2</sup>=4, 2<sup>3</sup>=8, 2<sup>4</sup>=16, 2<sup>5</sup>=323<sup>2</sup>=9, 3<sup>3</sup>=27, 3<sup>4</sup>=81, 3<sup>5</sup>=243
4<sup>2</sup>=16, 4<sup>3</sup>=64, 4<sup>4</sup>=256, 4<sup>5</sup>=1024
5<sup>2</sup>=25, 5<sup>3</sup>=125, 5<sup>4</sup>=625, 5<sup>5</sup>=3125
</div>If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
<div style='padding-left: 4em;'> 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125 </div>How many distinct terms are in the sequence generated by $a^b$ for 2 ≤ a ≤ n and 2 ≤ b ≤ n?
distinctPowers(15) should return a number.
assert(typeof distinctPowers(15) === 'number');
distinctPowers(15) should return 177.
assert.strictEqual(distinctPowers(15), 177);
distinctPowers(20) should return 324.
assert.strictEqual(distinctPowers(20), 324);
distinctPowers(25) should return 519.
assert.strictEqual(distinctPowers(25), 519);
distinctPowers(30) should return 755.
assert.strictEqual(distinctPowers(30), 755);
function distinctPowers(n) {
return n;
}
distinctPowers(30);
const distinctPowers = (n) => {
let list = [];
for (let a=2; a<=n; a++) {
for (let b=2; b<=n; b++) {
let term = Math.pow(a, b);
if (list.indexOf(term)===-1) list.push(term);
}
}
return list.length;
};