Question

Given a number n, write a program to find the sum of the largest prime factors of each of nine consecutive numbers starting from n. G(n) = f(n) + f(n+1) + f(n+2) + f(n+3) + f(n+4) + f(n+5) + f(n+6) + f(n+7) + f(n+8)

Answer 1

Given a number n, write a program to find the sum of the largest prime factors of each of nine consecutive numbers starting from n.

Explanation:

Python Program

def find_factors(num):

   #Accepts a number and returns the list of all the factors of a given number

   factors = []

   for i in range(2,(num+1)):

       if(num%i==0):

           factors.append(i)

   return factors

def is_prime(num, i):

   #Accepts the number num and num/2 --> i and returns True if the number is prime ,else returns False

   if(i==1):

       return True

   elif(num%i==0):

       return False;

   else:

       return(is_prime(num,i-1))

def find_largest_prime_factor(list_of_factors):

   large=[]

   for i in list_of_factors:

       if is_prime(i,i//2)==True:

           large.append(i)

   return max(large)

   #Accepts the list of factors and returns the largest prime factor

def find_f(num):

   #Accepts the number and returns the largest prime factor of the number

   f=find_factors(num)

   l=find_largest_prime_factor(f)

   return l

def find_g(num):

   #Accepts the number and returns the sum of the largest prime factors of the 9 consecutive numbers starting from the given number

   sum=0

   consicutive=[i for i in range(num,num+9)]

   for i in consicutive:

       largest_prime_factor=find_f(i)

       sum=sum+largest_prime_factor

   return sum

#call function

print(find_g(10))

Output

66