Problem F
Harshad Numbers
We’re all familiar with harshad numbers. For this problem, you will ... what’s that? You aren’t familiar with harshad numbers? They’re also known as Niven numbers – does that ring a bell?? Anything???
Well, it’s a simple enough concept. A harshad number is a number which is evenly divisible by the sum of its digits. For example, $24$ is a harshad number: the sum of its digits is $2+4=6$ and $24$ is divisible by $6$. $156$ is also a harshad number, since $1+5+6=12$ and $156 = (12)(13$). $157$ is NOT a harshad number since it is not divisible by $1+5+7=13$.
OK, let’s start over.
We’re all familiar with harshad numbers. For this problem, you will be given a number $n$ and must find the smallest harshad number $\geq n$.
Input
Input consists of a single line containing a positive integer $n \leq 1\, 000\, 000\, 000$.
Output
Display the smallest harshad number greater than or equal to $n$.
| Sample Input 1 | Sample Output 1 |
|---|---|
24 |
24 |
| Sample Input 2 | Sample Output 2 |
|---|---|
25 |
27 |
| Sample Input 3 | Sample Output 3 |
|---|---|
987654321 |
987654330 |
