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1. A Perfect Number N is a number whose sum of the proper divisors is equal to N. The proper divisors are the numbers that are evenly divisible to N from 1

to N-1. Example: 1 2 4 7 14 are the proper divisors of 28.

The sum of this number is 28, which is N itself, therefore, 28 is called a PERFECT NUMBER. If the sum of the proper divisors of N is less than N, then N is a Deficient Number. If the sum of the proper divisors of N is more than N, then N is Abundant Number.

Write a program that allows the user to enter the value of N and then displays the result indicating whether the number entered is perfect, deficient or abundant. Sample Run: Input a number: 16 The proper divisors of 16 are: 1 2 4 8 Sum of the proper divisors = 15 Therefore, 16 is a deficient number.

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I write an algorithm. You can write the program. This is a simple program. Not efficient in computation. you can replace the comparison K < N by K <= (N+1)/2 that is more efficient. It can be made more efficient by K < square root (N). But print K and N/K at the same time. output for N = 32 looks like 1 2 16 4 8 16

Algorithm Perfect begin

N: Integer - input data K : integer - current divisor Sum : integer - sum of factors

Print "Input a number : " Input N Print " The proper divisors of " , N, " are " K = 1 Sum = 0 While K <= N do If ( N % K ) = 0 then // reminder is 0. K<= (N+1)/2 is more efficient. Print K Sum = Sum + K end if K = K + 1 end while

print "Sum of the proper divisors is " , Sum , " Hence " , N

If (Sum = N ) then Print " is a perfect number " else if (Sum < N ) then Print " is a deficient number " else print " is an abundant number " end if