Description
While 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:
4937775= 3*5*5*65837
The sum of all digits of the telephone number is 4+9+3+7+7+7+5= 42,and the sum of the digits of its prime factors is equally 3+5+5+6+5+8+3+7=42. Wilansky was so amazed by his discovery that he named this kind 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, so he excluded them from the definition.
Wilansky published an article about Smith numbers in the Two Year College Mathematics Journal and 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 find a Smith number that was larger than the telephone number of his brother-in-law. It is your task to find Smith numbers that are larger than 4937775!
The sum of all digits of the telephone number is 4+9+3+7+7+7+5= 42,and the sum of the digits of its prime factors is equally 3+5+5+6+5+8+3+7=42. Wilansky was so amazed by his discovery that he named this kind 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, so he excluded them from the definition.
Wilansky published an article about Smith numbers in the Two Year College Mathematics Journal and 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 find a Smith number that was larger than the telephone number of his brother-in-law. It is your task to find Smith numbers that are larger than 4937775!
Input
The input file consists of a sequence of positive integers, one integer per line. Each integer will have at most 8 digits. The input is terminated by a line containing the number 0.
Output
For every number n > 0 in the input, you are to compute the smallest Smith number which is larger than n,and print it on a line by itself. You can assume that such a number exists.
Sample Input
4937774 0
Sample Output
4937775附上质因数分解的程序(用递归解决)#include <iostream> using namespace std; int sumOfDigits (int n){ int sum = 0; while(n){ sum += n % 10; n = n/10; } return sum; } int isprime(int n){ for(int i = 2;i * i <= n ;i++) if(n % i == 0) return 0; return 1; } int sumOfPrime(int n){ int sum = 0,i = 2; while(1){ if(n % i == 0){ sum += sumOfDigits(i); n = n / i; if(isprime(n)) break; }else{ i++; } } return sum += sumOfDigits(n); } int main() { int n; while(cin >> n && n){ while(1){ n++; if(!isprime(n)){ if(sumOfDigits(n) == sumOfPrime(n)){ cout << n << endl; break; } } } } return 0; }
#include <iostream> using namespace std; int isPrime(int n) { for(int i = 2;i * i <= n;i++) if(n % i == 0) return 0; return 1; } void prime(int n) { if(isPrime(n)){ cout << n << endl; return; } int i = 2; while(1){ if(n % i ==0){ cout << i << "*"; prime(n / i); break; } i++; } } int main() { int n; while(cin >> n){ prime(n); } return 0; }