53 lines
1.3 KiB
Markdown
53 lines
1.3 KiB
Markdown
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---
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id: 5900f4e51000cf542c50fff6
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title: 'Problem 374: Maximum Integer Partition Product'
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challengeType: 5
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forumTopicId: 302036
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dashedName: problem-374-maximum-integer-partition-product
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---
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# --description--
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An integer partition of a number n is a way of writing n as a sum of positive integers.
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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.
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The partitions of 5 into distinct parts are: 5, 4+1 and 3+2.
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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.
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So f(5)=6 and m(5)=2.
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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
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It can be verified that ∑f(n)·m(n) for 1 ≤ n ≤ 100 = 1683550844462.
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Find ∑f(n)·m(n) for 1 ≤ n ≤ 1014. Give your answer modulo 982451653, the 50 millionth prime.
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# --hints--
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`euler374()` should return 334420941.
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```js
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assert.strictEqual(euler374(), 334420941);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler374() {
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return true;
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}
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euler374();
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```
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# --solutions--
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```js
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// solution required
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```
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