Create sphenicNo.cpp

math/sphenicNo.cpp

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+//CODE ADAPTED FROM OTHER WEBSITE.
+// C++ program to check whether a number is a 
+// Sphenic number or not 
+#include<bits/stdc++.h> 
+using namespace std; 
+
+const int MAX = 1000; 
+
+// Create a vector to store least primes. 
+// Initialize all entries as 0. 
+vector<int> least_pf(MAX, 0); 
+
+// This function fills values in least_pf[]. 
+// such that the value of least_pf[i] stores 
+// smallest prime factor of i. 
+// This function is based on sieve of Eratosthenes 
+void leastPrimeFactor(int n) 
+{ 
+    // Least prime factor for 1 is 1 
+    least_pf[1] = 1; 
+
+    // Store least prime factor for all other 
+    // numbers. 
+    for (int i = 2; i <= n; i++) 
+    { 
+        // least_pf[i] == 0 means i is prime 
+        if (least_pf[i] == 0) 
+        { 
+            // Initializing prime number as its own 
+            // least prime factor. 
+            least_pf[i] = i; 
+
+            // Mark 'i' as a divisor for all its 
+            // multiples that are not already marked 
+            for (int j = 2*i; j <= n; j += i) 
+                if (least_pf[j] == 0) 
+                    least_pf[j] = i; 
+        } 
+    } 
+} 
+
+// Function returns true if n is a sphenic number and 
+// No otherwise 
+bool isSphenic(int n) 
+{ 
+    // Stores three prime factors of n. We have at-most 
+    // three elements in s. 
+    set<int> s; 
+
+    // Keep finding least prime factors until n becomes 1 
+    while (n > 1) 
+    { 
+        // Find least prime factor of current value of n. 
+        int lpf = least_pf[n]; 
+
+        // We store current size of s to check if a prime 
+        // factor repeats 
+        int init_size = s.size(); 
+
+        // Insert least prime factor of current value of n 
+        s.insert(lpf); 
+
+        // If either lpf repeats or number of lpfs becomes 
+        // more than 3, then return false. 
+        if (s.size() == init_size || s.size() > 3) 
+
+            // same prime divides the 
+            // number more than once 
+            return false; 
+
+        // Divide n by lpf 
+        n /= lpf; 
+    } 
+
+    // Return true if size of set is 3 
+    return (s.size() == 3); 
+} 
+
+int main() 
+{ 
+    leastPrimeFactor(MAX); 
+    for (int i=1; i<100; i++) 
+        if (isSphenic(i)) 
+           cout << i << " ";
+    return 0; 
+}