1. Definition

	An integer is called abundant if the sum of all its divisors 
	including 1 but excluding itself,  is greater than this number. When 
	this sum is equal to this number, the letter is called perfect. 
	If this sum is less then this number, it is called deficient. 

	Example:
	--------
	12 is abundant, and 8 is not abundant.
	
	

	2. Example in F90 language:
	
!This program tells whether a number is abundant
!-----------------------------------------------

PROGRAM abundant
IMPLICIT NONE
INTEGER :: i,n, sum
PRINT*,"Enter an integer : --> \n"
READ*, n

sum = 0
do i = 1, n-1
if (mod(n,i) == 0) THEN
sum = sum + i
end IF
continue

end do


if (sum. le. n) then
PRINT*,"The number", n," is  not abundant "

else
PRINT*,"The number", n," is  abundant "
endif

END PROGRAM abundant


	Results:
	--------
C:\\Fortran90>abundant
 Enter an integer : -->

8
 The number is not abundant 

C:\\Fortran90>abundant
 Enter an integer : -->

24
 The number 24 is  abundant 
 

 
 
!This program gives all the odd abundant integers less than a given one:
!------------------------------------------------------------------------

PROGRAM abundant_odd
IMPLICIT NONE
INTEGER :: j,i,n, sum
PRINT*,"Enter an integer : --> \n"
READ*, n

! To choose the numbers from 1 to n
do j =1,n
! To be odd
if (mod(j,2) /= 0) THEN

sum = 0
do i = 1, j
if (mod(j,i) == 0) THEN
sum = sum + i
end IF
continue

end do


if (sum -j. ge. j) then
PRINT*,"The number", j ," is abundant\n"
!else
!PRINT*,"The number", j," is  not abundant\n"

endif


! end first if
end if
! end first do
end do

END PROGRAM abundant_odd



	Results:
	--------
C:\\Fortran90>abundant
 Enter an integer : -->

8
 The number is not abundant 

C:\\Fortran90>abundant
 Enter an integer : -->

24
 The number 24 is  abundant 

C:\\Fortran90>abundant_odd
 Enter an integer : -->

5000
 The number 945 is abundant

 The number 1575 is abundant

 The number 2205 is abundant

 The number 2835 is abundant

 The number 3465 is abundant

 The number 4095 is abundant

 The number 4725 is abundant


C:\\Fortran90>