n and n+1 are integers with the same number of positive divisions. Find the integers n from 1

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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n and n+1 are integers with the same number of positive divisions. Find the integers n from 1<n<107. For example, the positive divisors of 14 are 1, 2, 7, 14, and 15 are 1, 3, 5, 15.

(P.s.: You have to done it by C++.)

Expert Solution
Step 1

Programming instructions:

 

  • Include the necessary header file.
  • In the main function, declare the required variables.
  • Use for-loop to call the divisorcount() function for each number.
  • Call the divisorcount() function for a number and store the value returned by the function in a variable.
  • Again all the divisorcount() function for a number less than the previous one store the value returned by the function in a variable.
  • Compare both the variables.
  • If they are equal print them.
  • The divisorcount() function counts the number of divisors for a number.
Step 2

Program:

 


// Header file
#include<stdio.h>

int divisorcount(int);


//Main function
int main()
{
    //Declare variables
    int n,divisor1,divisor2,j=0;

    //for-loop to call the function several times
    for(n=1;n<=107;n++){
        
        //Call the function for a number to count the number of divisors
        divisor1=divisorcount(n);
        
        //Call the same function for a number less than previous one
        divisor2=divisorcount(n-1);
        
        //Compare the numbers
        if(divisor1==divisor2){
            printf("%d and %d\n",n-1,n);
            j++;
        }
    }
    printf("\nThere are %d integers.",j);

}

//Function to count the number of divisors
int divisorcount(int num)
{
    int i,divi=0;
    for(i=1;i<=(num)/2;i++)
        if(num%i==0)
            divi++;
            
    return divi;
}

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