1.2 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4571000cf542c50ff69 | Problem 234: Semidivisible numbers | 5 | 301878 | problem-234-semidivisible-numbers |
--description--
For an integer n ≥ 4
, we define the lower prime square root of n
, denoted by lps(n)
, as the \text{largest prime} ≤ \sqrt{n}
and the upper prime square root of n
, ups(n)
, as the \text{smallest prime} ≥ \sqrt{n}
.
So, for example, lps(4) = 2 = ups(4)
, lps(1000) = 31
, ups(1000) = 37
.
Let us call an integer n ≥ 4
semidivisible, if one of lps(n)
and ups(n)
divides n
, but not both.
The sum of the semidivisible numbers not exceeding 15 is 30, the numbers are 8, 10 and 12. 15 is not semidivisible because it is a multiple of both lps(15) = 3
and ups(15) = 5
. As a further example, the sum of the 92 semidivisible numbers up to 1000 is 34825.
What is the sum of all semidivisible numbers not exceeding 999966663333?
--hints--
semidivisibleNumbers()
should return 1259187438574927000
.
assert.strictEqual(semidivisibleNumbers(), 1259187438574927000);
--seed--
--seed-contents--
function semidivisibleNumbers() {
return true;
}
semidivisibleNumbers();
--solutions--
// solution required