899 B
899 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f5411000cf542c510054 | Problem 468: Smooth divisors of binomial coefficients | 5 | 302143 | problem-468-smooth-divisors-of-binomial-coefficients |
--description--
An integer is called B-smooth if none of its prime factors is greater than B.
Let SB(n) be the largest B-smooth divisor of n. Examples: S1(10) = 1 S4(2100) = 12 S17(2496144) = 5712
Define F(n) = ∑1≤B≤n ∑0≤r≤n SB(C(n,r)). Here, C(n,r) denotes the binomial coefficient. Examples: F(11) = 3132 F(1 111) mod 1 000 000 993 = 706036312 F(111 111) mod 1 000 000 993 = 22156169
Find F(11 111 111) mod 1 000 000 993.
--hints--
euler468()
should return 852950321.
assert.strictEqual(euler468(), 852950321);
--seed--
--seed-contents--
function euler468() {
return true;
}
euler468();
--solutions--
// solution required