Sha 10042 Smith numbers (number theory)

Smith numbers
Backgroundwhile skimming his phone directory in 1982, Albert Wilansky, a mathematician of Lehigh University, noticed that the telephone number of his brother-in-law H. smith had the following peculiar property: the sum of the digits of that number was equal to the sum of the digits of the prime factors of that number. got it? Smith's telephone number was 493-7775. This number can be written as the product of its prime factors in the following way:

The sum of all digits of the telephone number is4 + 9 + 3 + 7 + 7 + 7 + 5 = 42, and the sum of the digits of its prime factors is calculated ly3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42. wilansky was so amazed by his discovery that he named this type of numbers after his brother-in-law: Smith numbers.

As this observation is also true for every prime number, Wilansky decided later that a (simple and unsophisticated) prime number is not worth being a Smith number and he excluded them from the definition.

Problemwilansky published an article about Smith numbers in Two year college mathematics JournalAnd was able to present a whole collection of different Smith numbers: for example, 9985 is a Smith number and so is 6036. however, Wilansky was not able to give a Smith number which was larger than the telephone number of his brother-in-law. it is your task to find Smith numbers which are larger than 4937775.

Inputthe input consists of several test cases, the number of which you are given in the first line of the input.

Each test case consists of one line containing a single positive integer smaller than 109.

Outputfor every input value N, You are to compute the smallest Smith number which is larger NAnd print each number on a single line. You can assume that such a number exists.

Sample Input

14937774

Sample output

4937775

If the sum of the numbers of a given number is equal to the sum of the numbers of all prime factors of the number, it is called the Smith number. Returns an N value and calculates the minimum number of Smith numbers greater than N.

Analysis: Perform prime factor decomposition on the number to be judged. Because the number is less than 10 ^ 9, if a number is a combination, there must be at least one element less than or equal to SQRT (10 ^ 9 ), you can save the prime numbers between 2-SQRT (10 ^ 9.

#include<stdio.h>#include<string.h>const int MAXN = 100005;int vis[MAXN], prime[10000], num;void get_prime(){    num = 0;    memset(vis, 0, sizeof(vis));    vis[0] = vis[1] = 1;    for(int i = 2; i < MAXN; i++)    {        if(!vis[i])        {            prime[num++] = i;            for(int j = i + i; j < MAXN; j += i)                vis[j] = 1;        }    }}bool is_prime(int x){    if(x == 0 || x == 1) return false;    if(x == 2) return true;    if(x % 2 == 0) return false;    for(int i = 3; i * i <= x; i += 2)        if(x % i == 0)            return false;    return true;}int sum(int x){    int res = 0;    while(x)    {        res += x % 10;        x /= 10;    }    return res;}int main(){    get_prime();    int n, t;    scanf("%d",&t);    while(t--)    {        scanf("%d",&n);        for(int i = n + 1; ; i++)        {            if(is_prime(i))                continue;            int s = 0, tmp = i, tmpsum = sum(i);            for(int j = 0; j < num; j++)            {                if(tmp % prime[j] == 0)                {                    while(tmp % prime[j] == 0)                    {                        s += sum(prime[j]);                        tmp /= prime[j];                    }                    if(is_prime(tmp))                    {                        s += sum(tmp);                        break;                    }                }            }            if(tmpsum == s)            {                printf("%d\n",i);                break;            }        }    }    return 0;}