1.7 KiB
1.7 KiB
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f40c1000cf542c50ff1e | Problem 159: Digital root sums of factorisations | 5 | 301790 | problem-159-digital-root-sums-of-factorisations |
--description--
A composite number can be factored many different ways.
For instance, not including multiplication by one, 24 can be factored in 7 distinct ways:
\begin{align}
& 24 = 2 \times 2 \times 2 \times 3\\\\
& 24 = 2 \times 3 \times 4 \\\\
& 24 = 2 \times 2 \times 6 \\\\
& 24 = 4 \times 6 \\\\
& 24 = 3 \times 8 \\\\
& 24 = 2 \times 12 \\\\
& 24 = 24
\end{align}$$
Recall that the digital root of a number, in base 10, is found by adding together the digits of that number, and repeating that process until a number arrives at less than 10. Thus the digital root of 467 is 8.
We shall call a Digital Root Sum (DRS) the sum of the digital roots of the individual factors of our number. The chart below demonstrates all of the DRS values for 24.
| Factorisation | Digital Root Sum |
|---------------|------------------|
| 2x2x2x3 | 9 |
| 2x3x4 | 9 |
| 2x2x6 | 10 |
| 4x6 | 10 |
| 3x8 | 11 |
| 2x12 | 5 |
| 24 | 6 |
The maximum Digital Root Sum of 24 is 11. The function $mdrs(n)$ gives the maximum Digital Root Sum of $n$. So $mdrs(24) = 11$.
Find $\sum{mdrs(n)}$ for $1 < n < 1,000,000$.
# --hints--
`euler159()` should return `14489159`.
```js
assert.strictEqual(euler159(), 14489159);
```
# --seed--
## --seed-contents--
```js
function euler159() {
return true;
}
euler159();
```
# --solutions--
```js
// solution required
```