---
id: 5900f46b1000cf542c50ff7d
challengeType: 5
title: '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?
## Instructions
## Tests
```yml
tests:
- text: euler254() should return 8184523820510.
testString: 'assert.strictEqual(euler254(), 8184523820510, ''euler254() should return 8184523820510.'');'
```
## Challenge Seed
```js
function euler254() {
// Good luck!
return true;
}
euler254();
```