freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-374-maximum-integer-partition-product.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4e51000cf542c50fff6	Problem 374: Maximum Integer Partition Product	5	302036	problem-374-maximum-integer-partition-product

--description--

An integer partition of a number n is a way of writing n as a sum of positive integers.

Partitions that differ only in the order of their summands are considered the same. A partition of n into distinct parts is a partition of n in which every part occurs at most once.

The partitions of 5 into distinct parts are:

5, 4 + 1 and 3 + 2.

Let f(n) be the maximum product of the parts of any such partition of n into distinct parts and let m(n) be the number of elements of any such partition of n with that product.

So f(5) = 6 and m(5) = 2.

For n = 10 the partition with the largest product is 10 = 2 + 3 + 5, which gives f(10) = 30 and m(10) = 3. And their product, f(10) \times m(10) = 30 \times 3 = 90

It can be verified that \sum f(n) \times m(n) for 1 ≤ n ≤ 100 = 1\\,683\\,550\\,844\\,462.

Find \sum f(n) \times m(n) for 1 ≤ n ≤ {10}^{14}. Give your answer modulo 982\\,451\\,653, the 50 millionth prime.

--hints--

maximumIntegerPartitionProduct() should return 334420941.

assert.strictEqual(maximumIntegerPartitionProduct(), 334420941);

--seed--

--seed-contents--

function maximumIntegerPartitionProduct() {

  return true;
}

maximumIntegerPartitionProduct();

--solutions--

// solution required