Given a number N, the task is to check whether the number is a Sublime number or not.
Sublime numbers are defined as positive numbers whose sum of positive divisors and count of positive divisors are both perfect numbers.
Examples:
Input: N = 12
Output: True
Explanation: 12 is a sublime number because its divisors are 1, 2, 3, 4, 6, and 12. So there are 6 factors of it and 6 is a perfect number and 1+2+3+4+6+12=28, which is also a perfect number. So 12 is a Sublime number.Input: N = 24
Output: False
Explanation: 24 is a not sublime number because the divisors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. So there are 8 factors and which is not a perfect number and 1+2+3+4+6+8+12+24=60, Which is not a perfect number. So 24 is not a Sublime number.
Approach: We have to implement two main logic:
- Find and Count Divisors of a Number Logic
- Perfect Number Checking.
Below are the steps involved in the implementation of the code:
- Initialize a number n.
- Find the divisors of the given number (n).
- Count the total number of divisors of the given number (n) and store it in a variable (count).
- Sum up the divisors, and store the result in a variable (sum).
- At last, check whether count and sum are perfect numbers or not.
- If both are perfect numbers, the given number (n) is a sublime number.
- Else, not a sublime number.
Below is the implementation of the code:
C++
// C++ Implementation to Check whether// a number is Sublime Number or Not.#include <iostream>using namespace std;// Check whether the number is// sublime or notvoid checkSublime(int num){ int s = 0, f = 0, s1 = 0, s2 = 0, i, j; for (i = 1; i <= num; i++) { if (num % i == 0) { // Finds the divisors // and sum up them s = s + i; // Counts the number // of divisors f++; } } // Check for perfect number for (j = 1; j < s; j++) { if (s % j == 0) s1 = s1 + j; } for (j = 1; j < f; j++) { if (f % j == 0) s2 = s2 + j; } if (s1 == s && s2 == f) cout << "True" << endl; else cout << "False" << endl;}// Driver codeint main(){ int n = 12; // Function call checkSublime(n); return 0;} |
Java
// java program to Check whether the number is sublime or// notpublic class SublimeNumber { // Check whether the number is sublime or not public static void checkSublime(int num) { int s = 0, f = 0, s1 = 0, s2 = 0, i, j; for (i = 1; i <= num; i++) { if (num % i == 0) { // Finds the divisors and sums them up s = s + i; // Counts the number of divisors f++; } } // Check for perfect number for (j = 1; j < s; j++) { if (s % j == 0) s1 = s1 + j; } for (j = 1; j < f; j++) { if (f % j == 0) s2 = s2 + j; } if (s1 == s && s2 == f) System.out.println("True"); else System.out.println("False"); } // Driver code public static void main(String[] args) { int n = 12; // Function call checkSublime(n); }}// This code is contributed by shivamgupta0987654321 |
Python3
# python3 Implementation to Check whether# a number is Sublime Number or Not.def checkSublime(num): s = 0 f = 0 s1 = 0 s2 = 0 for i in range(1, num+1): if num % i == 0: # Finds the divisors and sums them up s += i # Counts the number of divisors f += 1 # Check for perfect number for j in range(1, s): if s % j == 0: s1 += j for j in range(1, f): if f % j == 0: s2 += j if s1 == s and s2 == f: print("True") else: print("False")# Driver codeif __name__ == "__main__": n = 12 # Function call checkSublime(n)# This code is contributed by shivamgupta310570 |
C#
// C# Implementation to Check whether// a number is Sublime Number or Not.using System;public class SublimeNumber{ // Check whether the number is sublime or not public static void CheckSublime(int num) { int s = 0, f = 0, s1 = 0, s2 = 0, i, j; for (i = 1; i <= num; i++) { if (num % i == 0) { // Finds the divisors and sums them up s = s + i; // Counts the number of divisors f++; } } // Check for perfect number for (j = 1; j < s; j++) { if (s % j == 0) s1 = s1 + j; } for (j = 1; j < f; j++) { if (f % j == 0) s2 = s2 + j; } if (s1 == s && s2 == f) Console.WriteLine("True"); else Console.WriteLine("False"); } // Driver code public static void Main(string[] args) { int n = 12; // Function call CheckSublime(n); }} |
Javascript
// Check whether the number is// sublime or notfunction checkSublime(num) { let s = 0, f = 0, s1 = 0, s2 = 0; for (let i = 1; i <= num; i++) { if (num % i === 0) { // Finds the divisors // and sum up them s += i; // Counts the number // of divisors f++; } } // Check for perfect number for (let j = 1; j < s; j++) { if (s % j === 0) s1 += j; } for (let j = 1; j < f; j++) { if (f % j === 0) s2 += j; } if (s1 === s && s2 === f) console.log("True"); else console.log("False");}// Driver code const n = 12; // Function call checkSublime(n); |
Output
True
Time Complexity: O(N)
Auxiliary Space: O(1) as using constant variables
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