P –在给定范围内的平滑数

给定多个范围[L，R]和质数p，我们需要找到给定单个范围内的所有P平滑数。

What is P – smooth number?
An integer is P – smooth number if the largest Prime factor of that number <= p. 1 is considered (by OEIS) as P – smooth number for any possible value of P because it does not have any prime factor.

例子：

Input : p = 7   
        ranges[] = {[1, 17],  [10, 25]}

Output : 
For first range : 1 2 3 4 5 6 7 8 9 12 14 15 16
For second range : 15 16 18 20 21 24 25
Explanation : Largest prime factors of numbers
printed above are less than or equal to 7.

假设我们正在检查7 –平滑数字。
1.考虑一个整数56。这里56 = 2 * 2 * 2 * 7。
因此，56具有两个主因子(2和7)，这些主因子<= 7。因此，56是7平滑数字。
2.考虑另一个整数66。这里66 = 2 * 3 * 11。
66具有三个主要因子(2、3和11)。其中11> 7。所以66不是7平滑数字。

蛮力法：给出P和范围[L，R]。在这里L <=R。创建一个循环并检查所有包含[L：R]的数字。如果该数字的最大素数<= p。然后打印该号码(即P平滑号码)。使用maxPrimeDivisor(n)函数计算其最大素数/除数。高效方法：想法是预先计算p平滑数以获取所有范围的最大值。一旦我们进行了预先计算，我们就可以一张一张地快速打印所有范围。

# Python program to display p-smooth 
# number in given range.
# P-smooth numbers' array
p_smooth = [1] 
  
def maxPrimeDivisor(n):
      
    # Returns Maximum Prime 
    # Divisor of n
    MPD = -1
      
    if n == 1 : 
        return 1
      
    while n % 2 == 0:
        MPD = 2
        n = n // 2
      
    # math.sqrt(n) + 1
    size = int(n ** 0.5) + 1
    for odd in range( 3, size, 2 ):
        while n % odd == 0:
              
            # Make sure no multiples 
            # of prime, enters here
            MPD = odd
            n = n // odd
      
    # When n is prime itself
    MPD = max (n, MPD) 
      
    return MPD 
  
  
def generate_p_smooth(p, MAX_LIMIT):    
      
    # generates p-smooth numbers.
    global p_smooth
      
    for i in range(2, MAX_LIMIT + 1):
        if maxPrimeDivisor(i) <= p:
              
            # Satisfies the condition 
            # of p-smooth number
            p_smooth.append(i)
  
  
def find_p_smooth(L, R):
      
    # finds p-smooth number in the
    # given [L:R] range.
    global p_smooth
    if L <= p_smooth[-1]:
          
        # If user input exceeds MAX_LIMIT
        # range, no checking
        for w in p_smooth :
            if w > R : break
            if w >= L and w <= R :
                  
                # Print P-smooth numbers 
                # within range : L to R.
                print(w, end =" ")
                  
        print()
          
# p_smooth number : p = 7
# L <= R
p = 7
L, R = 1, 100
  
# Maximum possible value of R
MAX_LIMIT = 1000
  
# generate the p-smooth numbers
generate_p_smooth(p, MAX_LIMIT) 
  
# Find an print the p-smooth numbers
find_p_smooth(L, R)