1.8 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3c51000cf542c50fed6 | Problem 88: Product-sum numbers | 5 | 302203 | problem-88-product-sum-numbers |
--description--
A natural number, N, that can be written as the sum and product of a given set of at least two natural numbers, {a
1, a
2, ... , a
k} is called a product-sum number: N = a
1 + a
2 + ... + a
k = a
1 × a
2 × ... × a
k.
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=3: 6 = 1 × 2 × 3 = 1 + 2 + 3
k=4: 8 = 1 × 1 × 2 × 4 = 1 + 1 + 2 + 4
k=5: 8 = 1 × 1 × 2 × 2 × 2 = 1 + 1 + 2 + 2 + 2
k=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?
--hints--
productSumNumbers()
should return a number.
assert(typeof productSumNumbers() === 'number');
productSumNumbers()
should return 7587457.
assert.strictEqual(productSumNumbers(), 7587457);
--seed--
--seed-contents--
function productSumNumbers() {
return true;
}
productSumNumbers();
--solutions--
// solution required