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id	title	challengeType	forumTopicId	dashedName
5900f3891000cf542c50fe9c	Problem 29: Distinct powers	5	301941	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.

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);

--seed--

--seed-contents--

function distinctPowers(n) {

  return n;
}

distinctPowers(30);

--solutions--

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;
};

1.8 KiB Raw Blame History