yaworsw/euler-manager

---
:id: 88
:name: Product-sum numbers
:url: https://projecteuler.net/problem=88
:content: "A natural number, N, that can be written as the sum and product of a given
  set of at least two natural numbers, {_a_<sub>1</sub>, _a_<sub>2</sub>, ... , _a_<sub><i>k</i></sub>}
  is called a product-sum number: N = _a_<sub>1</sub> + _a_<sub>2</sub> + ... + _a_<sub><i>k</i></sub>
  = _a_<sub>1</sub> × _a_<sub>2</sub> × ... × _a_<sub><i>k</i></sub>.\n\nFor example,
  6 = 1 + 2 + 3 = 1 × 2 × 3.\n\nFor 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.\n\n_k_=2: 4 = 2 × 2 =
  2 + 2  \n_k_=3: 6 = 1 × 2 × 3 = 1 + 2 + 3  \n_k_=4: 8 = 1 × 1 × 2 × 4 = 1 + 1 +
  2 + 4  \n_k_=5: 8 = 1 × 1 × 2 × 2 × 2 = 1 + 1 + 2 + 2 + 2  \n_k_=6: 12 = 1 × 1 ×
  1 × 1 × 2 × 6 = 1 + 1 + 1 + 1 + 2 + 6\n\nHence 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.\n\nIn
  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.\n\nWhat is the sum of all the minimal product-sum
  numbers for 2≤_k_≤12000?\n\n"