---
id: 5900f46b1000cf542c50ff7d
title: 'Problem 254: Sums of Digit Factorials'
challengeType: 5
forumTopicId: 301902
dashedName: problem-254-sums-of-digit-factorials
---

# --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?

# --hints--

`euler254()` should return 8184523820510.

```js
assert.strictEqual(euler254(), 8184523820510);
```

# --seed--

## --seed-contents--

```js
function euler254() {

  return true;
}

euler254();
```

# --solutions--

```js
// solution required
```