903 B
903 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4e61000cf542c50fff9 | Problem 378: Triangle Triples | 5 | 302040 | problem-378-triangle-triples |
--description--
Let T(n)
be the n^{\text{th}}
triangle number, so T(n) = \frac{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) = 5\\,772
and Tr(1000) = 11\\,174\\,776
.
Find Tr(60\\,000\\,000)
. Give the last 18 digits of your answer.
--hints--
triangleTriples()
should return 147534623725724700
.
assert.strictEqual(triangleTriples(), 147534623725724700);
--seed--
--seed-contents--
function triangleTriples() {
return true;
}
triangleTriples();
--solutions--
// solution required