Question

Two positive integers are amicable if each prime divisor of one is a divisor of the other. Example: 6 and 12 are amicable, since each prime divisor of 6 (2 and 3) also divides 12, and each prime divisor of 12 (again 2 and 3) divides 6. Another: 12 and 15 are not amicable, since a prime divisor of 15 (namely 5) does not divide 12. Find the sum of all amicable pairs whose two members are both less than or equal to a given n using Phyton.

Answer 1

Python CODE ::

Execution ::...

Raw python code ::

_________________________________ amicable.py _________________________________

def isPrime(N): # Checks Prime or Not
   for i in range(2,N):
       if N%i == 0: # If there is a factor in between 2, n-1
           return False # then it is not a prime
   return True

def prime_factors(N): # Returns all prime factors
   fact = []
   for i in range(2,N+1): # 1 is not a prime factor so (2,N)
       if N%i == 0 :   # if it is factor
           if isPrime(i) :   # if it is a prime
               fact.append(i) # Appending to list
   return fact # Returning the list

def amicable(a,b): # Checks the amicable pair
   B = prime_factors(b)
   for f in B: # Checking all prime factors of 'b' for divisibility
       if a % f != 0: # with 'a'
           return False # if not returns False
   return True

n = int(input("Enter the n value : "))

print("amicable : ",end="")
Count = 0 ; Sum = 0
for a in range(1,n+1):
   for b in range(a+1,n+1):
       if amicable(a,b) and amicable(b,a):
           print("%s-%s,"%(a,b),end=" ")
           Count += 1 ; Sum += a+b
print("\n")
print("Number of amicable pairs :",Count)
print("Sum of amicable pairs :",Sum)

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