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# Hoax Number

Given a number ‘n’, check whether it is a hoax number or not.
A Hoax Number is defined as a composite number, whose sum of digits is equal to the sum of digits of its distinct prime factors. It may be noted here that, 1 is not considered a prime number, hence it is not included in the sum of digits of distinct prime factors.
Examples :

```Input : 22
Output : A Hoax Number
Explanation : The distinct prime factors of 22
are 2 and 11. The sum of their digits are 4,
i.e 2 + 1 + 1 and sum of digits of 22 is also 4.

Input : 84
Output : A Hoax Number
Explanation : The distinct prime factors of 84
are 2, 3 and 7. The sum of their digits are 12,
i.e 2 + 3 + 4 and sum of digits of 84 is also 12.

Input : 19
Output : Not a Hoax Number
Explanation : By definition, a hoax number is
a composite number.```

The definition of Hoax numbers bears close resemblance with the definition of Smith Numbers. In fact, some of the Hoax numbers are also Smith numbers. It is apparent that those hoax numbers that do not have repeated factors in their prime decomposition, i.e square free number are also eligible Smith numbers.
Implementation
1) First generate all distinct prime factors of the number ‘n’.
2) If the ‘n’ is not a prime number, find the sum of digits of the factors obtained in step 1.
3) Find the sum of digits of ‘n’.
4) Check if the sums obtained in steps 2 and 3 are equal or not.
5) If the sums are equal, ‘n’ is a hoax number.

## C++

 `// CPP code to check if a number is a hoax``// number or not.``#include ``using` `namespace` `std;``// Function to find distinct prime factors``// of given number n``vector<``int``> primeFactors(``int` `n)``{``    ``vector<``int``> res;``    ``if` `(n % 2 == 0) {``        ``while` `(n % 2 == 0)``            ``n = n / 2;``        ``res.push_back(2);``    ``}` `    ``// n is odd at this point, since it is no``    ``// longer divisible by 2. So we can test``    ``// only for the odd numbers, whether they``    ``// are factors of n``    ``for` `(``int` `i = 3; i <= ``sqrt``(n); i = i + 2) {` `        ``// Check if i is prime factor``        ``if` `(n % i == 0) {``            ``while` `(n % i == 0)``                ``n = n / i;``            ``res.push_back(i);``        ``}``    ``}` `    ``// This condition is to handle the case``    ``// when n is a prime number greater than 2``    ``if` `(n > 2)``        ``res.push_back(n);``    ``return` `res;``}` `// Function to calculate sum of digits of``// distinct prime factors of given number n``// and sum of digits of number n and compare``// the sums obtained``bool` `isHoax(``int` `n)``{``    ``// Distinct prime factors of n are being``    ``// stored in vector pf``    ``vector<``int``> pf = primeFactors(n);``    ` `    ``// If n is a prime number, it cannot be a``    ``// hoax number``    ``if` `(pf[0] == n)``        ``return` `false``;``    ` `    ``// Finding sum of digits of distinct prime``    ``// factors of the number n``    ``int` `all_pf_sum = 0;   ``    ``for` `(``int` `i = 0; i < pf.size(); i++) {` `        ``// Finding sum of digits in current``        ``// prime factor pf[i].``        ``int` `pf_sum;``        ``for` `(pf_sum = 0; pf[i] > 0;``             ``pf_sum += pf[i] % 10, pf[i] /= 10)``            ``;` `        ``all_pf_sum += pf_sum;``    ``}` `    ``// Finding sum of digits of number n``    ``int` `sum_n;``    ``for` `(sum_n = 0; n > 0; sum_n += n % 10,``                                  ``n /= 10)``        ``;` `    ``// Comparing the two calculated sums``    ``return` `sum_n == all_pf_sum;``}` `// Driver Method``int` `main()``{``    ``int` `n = 84;``    ``if` `(isHoax(n))``        ``cout << ``"A Hoax Number\n"``;``    ``else``        ``cout << ``"Not a Hoax Number\n"``;``    ``return` `0;``}`

## Java

 `// Java code to check if a number is``// a hoax number or not.``import` `java.io.*;``import` `java.util.*;` `public` `class` `GFG {``    ` `    ``// Function to find distinct``    ``// prime factors of given``    ``// number n``    ``static` `List primeFactors(``int` `n)``    ``{``        ``List res = ``new` `ArrayList();``        ``if` `(n % ``2` `== ``0``)``        ``{``            ``while` `(n % ``2` `== ``0``)``                ``n = n / ``2``;``            ``res.add(``2``);``        ``}``    ` `        ``// n is odd at this point,``        ``// since it is no longer``        ``// divisible by 2. So we``        ``// can test only for the``        ``// odd numbers, whether they``        ``// are factors of n``        ``for` `(``int` `i = ``3``; i <= Math.sqrt(n);``                                ``i = i + ``2``)``        ``{``    ` `            ``// Check if i is prime factor``            ``if` `(n % i == ``0``)``            ``{``                ``while` `(n % i == ``0``)``                    ``n = n / i;``                ``res.add(i);``            ``}``        ``}``    ` `        ``// This condition is to``        ``// handle the case when``        ``// n is a prime number``        ``// greater than 2``        ``if` `(n > ``2``)``            ``res.add(n);``        ``return` `res;``    ``}``    ` `    ``// Function to calculate``    ``// sum of digits of distinct``    ``// prime factors of given``    ``// number n and sum of``    ``// digits of number n and``    ``// compare the sums obtained``    ``static` `boolean` `isHoax(``int` `n)``    ``{``        ` `        ``// Distinct prime factors``        ``// of n are being``        ``// stored in vector pf``        ``List pf = primeFactors(n);``        ` `        ``// If n is a prime number,``        ``// it cannot be a hoax number``        ``if` `(pf.get(``0``) == n)``            ``return` `false``;``        ` `        ``// Finding sum of digits of distinct``        ``// prime factors of the number n``        ``int` `all_pf_sum = ``0``;``        ``for` `(``int` `i = ``0``; i < pf.size(); i++)``        ``{``    ` `            ``// Finding sum of digits in current``            ``// prime factor pf[i].``            ``int` `pf_sum;``            ``for` `(pf_sum = ``0``; pf.get(i) > ``0``;``                ``pf_sum += pf.get(i) % ``10``,``                   ``pf.set(i,pf.get(i) / ``10``));``    ` `            ``all_pf_sum += pf_sum;``        ``}``    ` `        ``// Finding sum of digits of number n``        ``int` `sum_n;``        ``for` `(sum_n = ``0``; n > ``0``; sum_n += n % ``10``,``                                    ``n /= ``10``)``            ``;``    ` `        ``// Comparing the two calculated sums``        ``return` `sum_n == all_pf_sum;``    ``}``    ` `    ``// Driver Code``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `n = ``84``;``        ``if` `(isHoax(n))``            ``System.out.print( ``"A Hoax Number\n"``);``        ``else``            ``System.out.print(``"Not a Hoax Number\n"``);``    ``}``}` `// This code is contributed by``// Manish Shaw (manishshaw1)`

## Python3

 `# Python3 code to check if a number is a hoax``# number or not.``import` `math` `# Function to find distinct prime factors``# of given number n``def` `primeFactors(n) :``    ``res ``=` `[]``    ``if` `(n ``%` `2` `=``=` `0``) :``        ``while` `(n ``%` `2` `=``=` `0``) :``            ``n ``=` `int``(n ``/` `2``)``        ``res.append(``2``)` `    ``# n is odd at this point, since it is no``    ``# longer divisible by 2. So we can test``    ``# only for the odd numbers, whether they``    ``# are factors of n``    ``for` `i ``in` `range``(``3``,``int``(math.sqrt(n)),``2``):``        ``# Check if i is prime factor``        ``if` `(n ``%` `i ``=``=` `0``) :``            ``while` `(n ``%` `i ``=``=` `0``) :``                ``n ``=` `int``(n ``/` `i)``            ``res.append(i)` `    ``# This condition is to handle the case``    ``# when n is a prime number greater than 2``    ``if` `(n > ``2``) :``        ``res.append(n)``    ``return` `res` `# Function to calculate sum of digits of``# distinct prime factors of given number n``# and sum of digits of number n and compare``# the sums obtained``def` `isHoax(n) :``    ``# Distinct prime factors of n are being``    ``# stored in vector pf``    ``pf ``=` `primeFactors(n)``    ` `    ``# If n is a prime number, it cannot be a``    ``# hoax number``    ``if` `(pf[``0``] ``=``=` `n) :``        ``return` `False``    ` `    ``# Finding sum of digits of distinct prime``    ``# factors of the number n``    ``all_pf_sum ``=` `0``    ``for` `i ``in` `range``(``0``,``len``(pf)):` `        ``# Finding sum of digits in current``        ``# prime factor pf[i].``        ``pf_sum ``=` `0``        ``while` `(pf[i] > ``0``):``            ``pf_sum ``+``=` `pf[i] ``%` `10``            ``pf[i] ``=` `int``(pf[i] ``/` `10``)` `        ``all_pf_sum ``+``=` `pf_sum``    `  `    ``# Finding sum of digits of number n``    ``sum_n ``=` `0``;``    ``while` `(n > ``0``):``        ``sum_n ``+``=` `n ``%` `10``        ``n ``=` `int``(n ``/` `10``)` `    ``# Comparing the two calculated sums``    ``return` `sum_n ``=``=` `all_pf_sum`  `# Driver Method``n ``=` `84``;``if` `(isHoax(n)):``    ``print` `(``"A Hoax Number\n"``)``else``:``    ``print` `(``"Not a Hoax Number\n"``)``    ` `# This code is contributed by Manish Shaw``# (manishshaw1)`

## C#

 `// C# code to check if a number is``// a hoax number or not.``using` `System;``using` `System.Collections.Generic;` `class` `GFG {``    ` `    ``// Function to find distinct``    ``// prime factors of given``    ``// number n``    ``static` `List<``int``> primeFactors(``int` `n)``    ``{``        ``List<``int``> res = ``new` `List<``int``>();``        ``if` `(n % 2 == 0)``        ``{``            ``while` `(n % 2 == 0)``                ``n = n / 2;``            ``res.Add(2);``        ``}``    ` `        ``// n is odd at this point,``        ``// since it is no longer``        ``// divisible by 2. So we``        ``// can test only for the``        ``// odd numbers, whether they``        ``// are factors of n``        ``for` `(``int` `i = 3; i <= Math.Sqrt(n);``                                ``i = i + 2)``        ``{``    ` `            ``// Check if i is prime factor``            ``if` `(n % i == 0)``            ``{``                ``while` `(n % i == 0)``                    ``n = n / i;``                ``res.Add(i);``            ``}``        ``}``    ` `        ``// This condition is to``        ``// handle the case when``        ``// n is a prime number``        ``// greater than 2``        ``if` `(n > 2)``            ``res.Add(n);``        ``return` `res;``    ``}``    ` `    ``// Function to calculate``    ``// sum of digits of distinct``    ``// prime factors of given``    ``// number n and sum of``    ``// digits of number n and``    ``// compare the sums obtained``    ``static` `bool` `isHoax(``int` `n)``    ``{``        ` `        ``// Distinct prime factors``        ``// of n are being``        ``// stored in vector pf``        ``List<``int``> pf = primeFactors(n);``        ` `        ``// If n is a prime number,``        ``// it cannot be a hoax number``        ``if` `(pf[0] == n)``            ``return` `false``;``        ` `        ``// Finding sum of digits of distinct``        ``// prime factors of the number n``        ``int` `all_pf_sum = 0;``        ``for` `(``int` `i = 0; i < pf.Count; i++)``        ``{``    ` `            ``// Finding sum of digits in current``            ``// prime factor pf[i].``            ``int` `pf_sum;``            ``for` `(pf_sum = 0; pf[i] > 0;``                ``pf_sum += pf[i] % 10, pf[i] /= 10);``    ` `            ``all_pf_sum += pf_sum;``        ``}``    ` `        ``// Finding sum of digits of number n``        ``int` `sum_n;``        ``for` `(sum_n = 0; n > 0; sum_n += n % 10,``                                     ``n /= 10)``            ``;``    ` `        ``// Comparing the two calculated sums``        ``return` `sum_n == all_pf_sum;``    ``}``    ` `    ``// Driver Code``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 84;``        ``if` `(isHoax(n))``            ``Console.Write( ``"A Hoax Number\n"``);``        ``else``            ``Console.Write(``"Not a Hoax Number\n"``);``    ``}``}` `// This code is contributed by``// Manish Shaw (manishshaw1)`

## PHP

 ` 2)``        ``array_push``(``\$res``, ``\$n``);``    ``return` `\$res``;``}` `// Function to calculate sum``// of digits of distinct prime``// factors of given number n``// and sum of digits of number``// n and compare the sums obtained``function` `isHoax(``\$n``)``{``    ``// Distinct prime factors``    ``// of n are being stored``    ``// in vector pf``    ``\$pf` `= primeFactors(``\$n``);``    ` `    ``// If n is a prime number,``    ``// it cannot be a hoax number``    ``if` `(``\$pf``[0] == ``\$n``)``        ``return` `false;``    ` `    ``// Finding sum of digits of distinct``    ``// prime factors of the number n``    ``\$all_pf_sum` `= 0;``    ``for` `(``\$i` `= 0; ``\$i` `< ``count``(``\$pf``); ``\$i``++)``    ``{` `        ``// Finding sum of digits in``        ``// current prime factor pf[i].``        ``\$pf_sum``;``        ``for` `(``\$pf_sum` `= 0; ``\$pf``[``\$i``] > 0;``              ``\$pf_sum` `+= ``\$pf``[``\$i``] % 10,``                       ``\$pf``[``\$i``] /= 10)``            ``;` `        ``\$all_pf_sum` `+= ``\$pf_sum``;``    ``}` `    ``// Finding sum of digits of number n``    ``for` `(``\$sum_n` `= 0; ``\$n` `> 0;``          ``\$sum_n` `+= ``\$n` `% 10, ``\$n` `/= 10)``        ``;` `    ``// Comparing the two calculated sums``    ``return` `\$sum_n` `== ``\$all_pf_sum``;``}` `// Driver Code``\$n` `= 84;``if` `(isHoax(``\$n``))``    ``echo` `(``"A Hoax Number\n"``);``else``    ``echo` `(``"Not a Hoax Number\n"``);``    ` `// This code is contributed by``// Manish Shaw(manishshaw1)``?>`

## Javascript

 ``

Output :

`A Hoax Number`

Time Complexity: O(√n log n)
Auxiliary Space: O(n)

Please suggest if someone has a better solution which is more efficient in terms of space and time.