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

id, challengeType, isHidden, title, forumTopicId

id	challengeType	isHidden	title	forumTopicId
5900f4e51000cf542c50fff6	5	false	Problem 374: Maximum Integer Partition Product	302036

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)·m(10) = 30·3 = 90

It can be verified that ∑f(n)·m(n) for 1 ≤ n ≤ 100 = 1683550844462.

Find ∑f(n)·m(n) for 1 ≤ n ≤ 1014. Give your answer modulo 982451653, the 50 millionth prime.

Instructions

Tests

tests:
  - text: <code>euler374()</code> should return 334420941.
    testString: assert.strictEqual(euler374(), 334420941);

Challenge Seed

function euler374() {
  // Good luck!
  return true;
}

euler374();

Solution

// solution required