---
id: 5900f3c51000cf542c50fed6
challengeType: 5
title: 'Problem 88: Product-sum numbers'
---

## Description
<section id='description'>
A natural number, N, that can be written as the sum and product of a given set of at least two natural numbers, {a1, a2, ... , ak} is called a product-sum number: N = a1 + a2 + ... + ak = a1 × a2 × ... × ak.
For example, 6 = 1 + 2 + 3 = 1 × 2 × 3.
For a given set of size, k, we shall call the smallest N with this property a minimal product-sum number. The minimal product-sum numbers for sets of size, k = 2, 3, 4, 5, and 6 are as follows.
k=2: 4 = 2 × 2 = 2 + 2k=3: 6 = 1 × 2 × 3 = 1 + 2 + 3k=4: 8 = 1 × 1 × 2 × 4 = 1 + 1 + 2 + 4k=5: 8 = 1 × 1 × 2 × 2 × 2  = 1 + 1 + 2 + 2 + 2k=6: 12 = 1 × 1 × 1 × 1 × 2 × 6 = 1 + 1 + 1 + 1 + 2 + 6
Hence for 2≤k≤6, the sum of all the minimal product-sum numbers is 4+6+8+12 = 30; note that 8 is only counted once in the sum.
In fact, as the complete set of minimal product-sum numbers for 2≤k≤12 is {4, 6, 8, 12, 15, 16}, the sum is 61.
What is the sum of all the minimal product-sum numbers for 2≤k≤12000?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler88()</code> should return 7587457.
    testString: assert.strictEqual(euler88(), 7587457, '<code>euler88()</code> should return 7587457.');

```

</section>

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

<div id='js-seed'>

```js
function euler88() {
  // Good luck!
  return true;
}

euler88();
```

</div>



</section>

## Solution
<section id='solution'>

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