GOOD NUMBERS

• Problem Description

  
  A number is called a square free number if there does not exist a number greater than 1, whose square divides the number evenly/perfectly. For example, number 8 is not a square free number as number 4 (which is square of 2), divides 8. Similarly, number 4 is also not a square free number. However numbers 1, 3, 6 all are square free numbers. 
  
  A number n is called a good number if following properties hold. 
  It is a square free number.
  
  Let s denote the sum of all divisors of n (including non-trivial divisors like 1 and itself). Let c denote the number of prime numbers dividing s. Number c should be a prime number.
  You will enter two numbers L, R, you have to find sum of divisors (including non-trivial) of all the good numbers in the range L to R, both inclusive. 
  Please note that 0 is not considered a prime number

• CODING ARENA

• #include <stdio.h>

  #include<math.h>

  int squarefree(int n);

  int prime(int l);

  int sum(int k);

  int primesum(int m);

  int main()

  {

    int t;

    int a,b,i;

    long long int ans=0,k;

    scanf("%d",&t);

    long long int s[100001]={0};

    for(i=5;i<100001;i++)

    {

      if(squarefree(i)==0 && prime(primesum(sum(i)))==1)

      {

        ans+=sum(i);

      }

      s[i]=ans;

    }

    while(t--)

    {

      scanf("%d%d",&a,&b);

      k=s[b]-s[a-1];

      printf("%lli\n",k);

    }

    return 0;

  }

  
  

  int primesum(int m)

  {

    int sum=0,i,k,j;

    j=sqrt(m);

    for(i=1;i<=j;i++)

    {

      if(m%i==0)

      {

        k=m/i;

        if(prime(i))

          sum++;

        if(k!=i && m%k==0 && prime(k))

        {

          sum++;

        }

      }

    }

    return sum;

  }

  
  

  int prime(int l)

  {

    int j,flag=1;

    if(l==1)

      return 0;

    if(l==2)

      return 1;

    if(l%2==0)

      flag=0;

    if(flag==1)

    {

      for(j=3;j<sqrt(l);j+=2)

      {

        if(l%j==0)

        {

          flag=0;

          break;

        }

      }

         }

      return flag;

  }

  int squarefree(int n)

  {

    int i,j,flag=0,k;

    i=sqrt(n);

    for(j=2;j<=i;j++)

    {

      k=j*j;

      if(n%k==0)

        flag=1;

    }

    return flag;

  }

  int sum(int k)

  {

    int i,sum=0,j;

    for(i=1;i<sqrt(k);i++)

    {

      if(k%i==0)

      {

        sum+=i;

        j=k/i;

        if(j!=i)

          sum+=j;

      }

    }

    return sum;

  }

• 
  

• Test Case 1

  
  Input (stdin)

  2
  
  1 5
  
  6 10
  
  

  Expected Output

  6
  
  30

• Test Case 2

  
  Input (stdin)

  2
  
  5 1
  
  8 12
  
  

  Expected Output

  0
  
  30