# 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.

1
by angelikamoldz

2014-09-24T03:52:00+05:30

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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

end perfect
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