一个Sphenic Number是一个正整数n ，它是三个不同素数的乘积。前几个数字分别是30、42、66、70、78、102、105、110、114，…
给定一个数字n ，确定它是否是一个Sphenic Number。
例子：
Input : 30
Output : Yes
Explanation : 30 is the smallest Sphenic number,
30 = 2 × 3 × 5
the product of the smallest three primes
Input : 60
Output : No
Explanation : 60 = 22 x 3 x 5
has exactly 3 prime factors but
is not a sphenic number可以通过以下事实检查斜数：每个斜数将具有正好为8的除数SPHENIC NUMBER
所以首先我们将尝试找出数字是否正好有8个除数，如果不是，则简单地回答否;如果正好有8个除数，则我们将确定1之后的前3位数字是否为质数。
例如。 30(折号)
30 = p * q * r(即p，q和r是三个不同的素数no，它们的乘积是30)
除数的集合是(1,2,3,5,6,10,15,30)。
以下是该想法的实现。
C++
// C++ program to check whether a number is a
// Sphenic number or not
#include
using namespace std;
//create a global array of size 10001;
bool arr[1001];
// This functions finds all primes smaller than 'limit'
// using simple sieve of eratosthenes.
void simpleSieve()
{
// initialize all entries of it as true. A value
// in mark[p] will finally be false if 'p' is Not
// a prime, else true.
memset(arr,true,sizeof(arr));
// One by one traverse all numbers so that their
// multiples can be marked as composite.
for(int p=2;p*p<1001;p++)
{
// If p is not changed, then it is a prime
if(arr[p])
{// Update all multiples of p
for(int i=p*2;i<1001;i=i+p)
arr[i]=false;
}
}
}
int find_sphene(int N)
{
int arr1[8]={0}; //to store the 8 divisors
int count=0; //to count the number of divisor
int j=0;
for(int i=1;i<=N;i++)
{
if(N%i==0 &&count<9)
{
count++;
arr1[j++]=i;
}
}
//finally check if there re 8 divisor and all the numbers are distinct prime no return 1
//else return 0
if(count==8 && (arr[arr1[1]] && arr[arr1[2]] && arr[arr1[3]]))
return 1;
return 0;
}
// Driver program to test above function
int main()
{
int n = 60;
simpleSieve();
int ans=find_sphene(n);
if(ans)
cout<<"Yes";
else
cout<<"NO";
} Java
// Java program to check whether a number is a
// Sphenic number or not
import java.util.*;
class GFG
{
// create a global array of size 10001;
static boolean []arr = new boolean[1001];
// This functions finds all primes smaller than 'limit'
// using simple sieve of eratosthenes.
static void simpleSieve()
{
// initialize all entries of it as true. A value
// in mark[p] will finally be false if 'p' is Not
// a prime, else true.
Arrays.fill(arr, true);
// One by one traverse all numbers so that their
// multiples can be marked as composite.
for(int p = 2; p * p < 1001; p++)
{
// If p is not changed, then it is a prime
if(arr[p])
{
// Update all multiples of p
for(int i = p * 2; i < 1001; i = i + p)
arr[i] = false;
}
}
}
static int find_sphene(int N)
{
int []arr1 = new int[8]; // to store the 8 divisors
int count = 0; // to count the number of divisor
int j = 0;
for(int i = 1; i <= N; i++)
{
if(N % i == 0 && count < 8)
{
count++;
arr1[j++] = i;
}
}
// finally check if there re 8 divisor and
// all the numbers are distinct prime no return 1
// else return 0);
if(count == 8 && (arr[arr1[1]] && arr[arr1[2]] && arr[arr1[3]]))
return 1;
return 0;
}
// Driver code
public static void main(String[] args)
{
int n = 60;
simpleSieve();
int ans = find_sphene(n);
if(ans == 1)
System.out.print("Yes");
else
System.out.print("NO");
}
}
// This code is contributed by aashish1995Python3
# Python3 program to check whether a number
# is a Sphenic number or not
# Create a global array of size 1001;
arr = [True] * (1001)
# This functions finds all primes smaller
# than 'limit' using simple sieve of
# eratosthenes.
def simpleSieve():
# Initialize all entries of it as
# True. A value in mark[p] will
# finally be False if 'p' is Not
# a prime, else True.
k = 0
# One by one traverse all numbers so
# that their multiples can be marked
# as composite.
for p in range(2, 1001):
if (p * p > 1001):
break
# If p is not changed, then it is a prime
if (arr[p]):
# Update all multiples of p
for k in range(p, 1001, k + p):
arr[k] = False
def find_sphene(N):
# To store the 8 divisors
arr1 = [0] * (8)
# To count the number of divisor
count = 0
j = 0
for i in range(1, N + 1):
if (N % i == 0 and count < 8):
count += 1
arr1[j] = i
j += 1
# Finally check if there re 8 divisor and
# all the numbers are distinct prime no return 1
# else return 0);
if (count == 8 and (arr[arr1[1]] and
arr[arr1[2]] and arr[arr1[3]])):
return 1;
return 0;
# Driver code
if __name__ == '__main__':
n = 60
simpleSieve()
ans = find_sphene(n)
if (ans == 1):
print("Yes")
else:
print("NO")
# This code is contributed by gauravrajput1C#
// C# program to check whether a number
// is a Sphenic number or not
using System;
class GFG{
// Create a global array of size 10001;
static bool []arr = new bool[1001];
// This functions finds all primes smaller than
// 'limit'. Using simple sieve of eratosthenes.
static void simpleSieve()
{
// Initialize all entries of it as true.
// A value in mark[p] will finally be
// false if 'p' is Not a prime, else true.
for(int i = 0;i<1001;i++)
arr[i] = true;
// One by one traverse all numbers so
// that their multiples can be marked
// as composite.
for(int p = 2; p * p < 1001; p++)
{
// If p is not changed, then it
// is a prime
if (arr[p])
{
// Update all multiples of p
for(int i = p * 2; i < 1001; i = i + p)
arr[i] = false;
}
}
}
static int find_sphene(int N)
{
// To store the 8 divisors
int []arr1 = new int[8];
// To count the number of divisor
int count = 0;
int j = 0;
for(int i = 1; i <= N; i++)
{
if (N % i == 0 && count < 8)
{
count++;
arr1[j++] = i;
}
}
// Finally check if there re 8 divisor
// and all the numbers are distinct prime
// no return 1 else return 0);
if (count == 8 && (arr[arr1[1]] &&
arr[arr1[2]] && arr[arr1[3]]))
return 1;
return 0;
}
// Driver code
public static void Main(String[] args)
{
int n = 60;
simpleSieve();
int ans = find_sphene(n);
if (ans == 1)
Console.Write("Yes");
else
Console.Write("NO");
}
}
// This code is contributed by aashish1995Javascript
输出：
NO参考：
1. OEIS
2. https://en.wikipedia.org/wiki/Sphenic_number