# Problem 278: Linear Combinations of Semiprimes
Given the values of integers 1 < a1 < a2 <... < an, consider
the linear combinationq1a1 + q2a2 + ... + qnan = b, using only integer
values qk ≥ 0. Note that for a given set of ak, it may be that not all
values of b are possible. For instance, if a1 = 5 and a2 = 7, there are
no q1 ≥ 0 and q2 ≥ 0 such that b could be 1, 2, 3, 4, 6, 8, 9, 11, 13,
16, 18 or 23. In fact, 23 is the largest impossible value of b for a1 =
5 and a2 = 7. We therefore call f(5, 7) = 23. Similarly, it can be shown
that f(6, 10, 15)=29 and f(14, 22, 77) = 195. Find ∑ f(p\*q,p\*r,q\*r),
where p, q and r are prime numbers and p < q < r < 5000.