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id	challengeType	title	forumTopicId
5900f4e61000cf542c50fff9	5	Problem 378: Triangle Triples	302040

Description

Let T(n) be the nth triangle number, so T(n) =

n (n+1)2

Let dT(n) be the number of divisors of T(n). E.g.: T(7) = 28 and dT(7) = 6.

Let Tr(n) be the number of triples (i, j, k) such that 1 ≤ i < j < k ≤ n and dT(i) > dT(j) > dT(k). Tr(20) = 14, Tr(100) = 5772 and Tr(1000) = 11174776.

Find Tr(60 000 000). Give the last 18 digits of your answer.

Instructions

Tests

tests:
  - text: <code>euler378()</code> should return 147534623725724700.
    testString: assert.strictEqual(euler378(), 147534623725724700);

Challenge Seed

function euler378() {

  return true;
}

euler378();

Solution

// solution required

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