yaworsw/euler-manager

---
:id: 278
:name: Linear Combinations of Semiprimes
:url: https://projecteuler.net/problem=278
:content: "Given the values of integers 1 \\< <var>a</var><sub>1</sub> \\< <var>a</var><sub>2</sub>
  \\<... \\< <var>a</var><sub><var>n</var></sub>, consider the linear combination
  \ \n<var>q</var><sub>1</sub><var>a</var><sub>1</sub> + <var>q</var><sub>2</sub><var>a</var><sub>2</sub>
  + ... + <var>q</var><sub><var>n</var></sub><var>a</var><sub><var>n</var></sub> =
  <var>b</var>, using only integer values <var>q</var><sub><var>k</var></sub> ≥ 0.\n\nNote
  that for a given set of <var>a</var><sub><var>k</var></sub>, it may be that not
  all values of <var>b</var> are possible.  \nFor instance, if <var>a</var><sub>1</sub>
  = 5 and <var>a</var><sub>2</sub> = 7, there are no <var>q</var><sub>1</sub> ≥ 0
  and <var>q</var><sub>2</sub> ≥ 0 such that <var>b</var> could be  \n 1, 2, 3, 4,
  6, 8, 9, 11, 13, 16, 18 or 23.  \nIn fact, 23 is the largest impossible value of
  <var>b</var> for <var>a</var><sub>1</sub> = 5 and <var>a</var><sub>2</sub> = 7.
  \ \n We therefore call <var>f</var>(5, 7) = 23.  \n Similarly, it can be shown that
  <var>f</var>(6, 10, 15)=29 and <var>f</var>(14, 22, 77) = 195.\n\nFind ∑ <var>f</var>(<var>p*q,p*r,q*r</var>),
  where <var>p</var>, <var>q</var> and <var>r</var> are prime numbers and <var>p</var>
  &lt <var>q</var> \\< <var>r</var> \\< 5000.\n\n"