yaworsw/euler-manager

---
:id: 374
:name: Maximum Integer Partition Product
:url: https://projecteuler.net/problem=374
:content: "An integer partition of a number <var>n</var> is a way of writing <var>n</var>
  as a sum of positive integers.\n\nPartitions that differ only in the order of their
  summands are considered the same. A partition of <var>n</var> into **distinct parts**
  is a partition of <var>n</var> in which every part occurs at most once.\n\nThe partitions
  of 5 into distinct parts are:  \n5, 4+1 and 3+2.\n\nLet f(<var>n</var>) be the maximum
  product of the parts of any such partition of <var>n</var> into distinct parts and
  let m(<var>n</var>) be the number of elements of any such partition of <var>n</var>
  with that product.\n\nSo f(5)=6 and m(5)=2.\n\nFor <var>n</var>=10 the partition
  with the largest product is 10=2+3+5, which gives f(10)=30 and m(10)=3.  \nAnd their
  product, f(10)·m(10) = 30·3 = 90\n\nIt can be verified that  \n∑f(<var>n</var>)·m(<var>n</var>)
  for 1 ≤ <var>n</var> ≤ 100 = 1683550844462.\n\nFind ∑f(<var>n</var>)·m(<var>n</var>)
  for 1 ≤ <var>n</var> ≤ 10<sup>14</sup>.  \nGive your answer modulo 982451653, the
  50 millionth prime.\n\n"