---
id: 5900f46b1000cf542c50ff7d
challengeType: 5
title: 'Problem 254: Sums of Digit Factorials'
---

## Description
<section id='description'>
Define f(n) as the sum of the factorials of the digits of n. For example, f(342) = 3! + 4! + 2! = 32.

Define sf(n) as the sum of the digits of f(n). So sf(342) = 3 + 2 = 5.

Define g(i) to be the smallest positive integer n such that sf(n) = i. Though sf(342) is 5, sf(25) is also 5, and it can be verified that g(5) is 25.

Define sg(i) as the sum of the digits of g(i). So sg(5) = 2 + 5 = 7.

Further, it can be verified that g(20) is 267 and ∑ sg(i) for 1 ≤ i ≤ 20 is 156.

What is ∑ sg(i) for 1 ≤ i ≤ 150?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler254()</code> should return 8184523820510.
    testString: 'assert.strictEqual(euler254(), 8184523820510, "<code>euler254()</code> should return 8184523820510.");'

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler254() {
  // Good luck!
  return true;
}

euler254();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>