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id	title	challengeType	forumTopicId	dashedName
5900f4831000cf542c50ff95	Problem 278: Linear Combinations of Semiprimes	5	301928	problem-278-linear-combinations-of-semiprimes

--description--

Given the values of integers 1 < a_1 < a_2 < \ldots < a_n, consider the linear combination q_1a_1 + q_2a_2 + \ldots + q_na_n = b, using only integer values q_k ≥ 0.

Note that for a given set of a_k, it may be that not all values of b are possible. For instance, if a_1 = 5 and a_2 = 7, there are no q_1 ≥ 0 and q_2 ≥ 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 a_1 = 5 and a_2 = 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 \sum f(pq,pr,qr), where p, q and r are prime numbers and p < q < r < 5000.

--hints--

linearCombinationOfSemiprimes() should return 1228215747273908500.

assert.strictEqual(linearCombinationOfSemiprimes(), 1228215747273908500);

--seed--

--seed-contents--

function linearCombinationOfSemiprimes() {

  return true;
}

linearCombinationOfSemiprimes();

--solutions--

// solution required

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