--description--

Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

8208 = 8⁴ + 2⁴ + 0⁴ + 8⁴

9474 = 9⁴ + 4⁴ + 7⁴ + 4⁴

As 1 = 1⁴ is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of n powers of their digits.

--hints--

digitnPowers(2) should return a number.

assert(typeof digitnPowers(2) === 'number');

digitnPowers(2) should return 0.

assert(digitnPowers(2) == 0);

digitnPowers(3) should return 1301.

assert(digitnPowers(3) == 1301);

digitnPowers(4) should return 19316.

assert(digitnPowers(4) == 19316);

digitnPowers(5) should return 443839.

assert(digitnPowers(5) == 443839);

--seed--

--seed-contents--

function digitnPowers(n) {

  return n;
}

digitnPowers(5);

--solutions--

// solution required