$1.$ a$).$ A perfect number is a positive integer that is equal to the sum of its proper divisors $($excluding the

number itself$).$ For example, $6$ is a perfect number because $1+2+3=6.$ Implement an algorithm to

determine the given no N is perfect number or not.

b$)$ i$)$ Develop a C program to check if a given number N is a perfect number or not, if N is a perfect

number or not.

ii$)$ Develop a C program to count the number of factors of the above result and determine how many of

these factors are even and how many are odd and how many are prime.

c$)$Develop a c program to calculate the sum of perfect numbers between $1$ to $100$ and Calculate the

average of the sums of the prime factors for all the perfect numbers found.

d$)$ Amicable numbers are two different numbers so related that the sum of the proper divisors

of each is equal to the other number. For example, $(220,284)$ is a pair of amicable numbers.

Develop a program to find all pairs of amicable numbers below a given limit $1000.$