1.2 KiB
1.2 KiB
| 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:
\begin{align}
& S_1(10) = 1 \\\\
& S_4(2\\,100) = 12 \\\\
& S_{17}(2\\,496\\,144) = 5\\,712
\end{align}$$
Define $F(n) = \displaystyle\sum_{B = 1}^n \sum_{r = 0}^n S_B(\displaystyle\binom{n}{r})$. Here, $\displaystyle\binom{n}{r}$ denotes the binomial coefficient.
Examples:
$$\begin{align}
& F(11) = 3132 \\\\
& F(1\\,111)\bmod 1\\,000\\,000\\,993 = 706\\,036\\,312 \\\\
& F(111\\,111)\bmod 1\\,000\\,000\\,993 = 22\\,156\\,169
\end{align}$$
Find $F(11\\,111\\,111)\bmod 1\\,000\\,000\\,993$.
# --hints--
`smoothDivisorsOfBinomialCoefficients()` should return `852950321`.
```js
assert.strictEqual(smoothDivisorsOfBinomialCoefficients(), 852950321);
```
# --seed--
## --seed-contents--
```js
function smoothDivisorsOfBinomialCoefficients() {
return true;
}
smoothDivisorsOfBinomialCoefficients();
```
# --solutions--
```js
// solution required
```