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Friendly Pair
Here we will discuss how to check whether a pair of numbers is a Friendly Pair or not. In number theory, friendly pairs are two numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself i.e ?(n)/n. S o, two number n and m are friendly number if
?(n)/n = ?(m)/m.
where ?(n) is the sum of divisors of n.
Example:
- n=6 , m=28
- Divisor of 6 are 1, 2, 3, 6.
Divisor of 28 are 1, 2, 4, 7, 14, 28. Sum of divisor of 6 and 28 are 12 and 56 respectively. Abundancy index of 6 and 28 are 2. So they are friendly pair.
- Divisor of 6 are 1, 2, 3, 6.
- n=18 , m=7
- They are not friendly pair.


Implementation:
- Find the sum of divisors of n and then of m .
- Find the abundancy idex of both the number say x and y.
- If x==y then it is Friendly pair else not .
Python Code:
#’Enter the numbers to check’
n=int(input())
m=int(input())
import math
sum_n=1 + n #sum of divisor of n
sum_m=1 + m #sum of divisor of m
i=2
j=2
#finding divisor
while(i<=math.sqrt(n)):
if(n%i==0):
if(n//i==i):
sum_n+=i
else:
sum_n+=i + n//i
i=i+1
while(j<=math.sqrt(m)):
if(m%j==0):
if(m//j==j):
sum_m+=j
else:
sum_m+=j + m//j
j=j+1
if(sum_n/n==sum_m/m):
print(‘Yes’ , n , ‘,’ , m ,‘ are friendly Pair’)
else:
print(‘No’, n , ‘,’ , m ,‘ are not friendly Pair’)
Input:
6
28
Output:
Yes 6 , 28 are friendly Pair
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