---
id: 5900f3891000cf542c50fe9c
title: 'Problem 29: Distinct powers'
challengeType: 5
forumTopicId: 301941
dashedName: problem-29-distinct-powers
---
# --description--
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`?
# --hints--
`distinctPowers(15)` should return a number.
```js
assert(typeof distinctPowers(15) === 'number');
```
`distinctPowers(15)` should return 177.
```js
assert.strictEqual(distinctPowers(15), 177);
```
`distinctPowers(20)` should return 324.
```js
assert.strictEqual(distinctPowers(20), 324);
```
`distinctPowers(25)` should return 519.
```js
assert.strictEqual(distinctPowers(25), 519);
```
`distinctPowers(30)` should return 755.
```js
assert.strictEqual(distinctPowers(30), 755);
```
# --seed--
## --seed-contents--
```js
function distinctPowers(n) {
return n;
}
distinctPowers(30);
```
# --solutions--
```js
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;
};
```