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Abundant Numbers

Sam Benry
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Joined: Mar 21, 2008
Posts: 89
A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.

A number whose proper divisors are less than the number is called deficient and a number whose proper divisors exceed the number is called abundant.

As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest number that can be written as the sum of two abundant numbers is 24. By mathematical analysis, it can be shown that all integers greater than 28123 can be written as the sum of two abundant numbers. However, this upper limit cannot be reduced any further by analysis even though it is known that the greatest number that cannot be expressed as the sum of two abundant numbers is less than this limit.

Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.


I wrote the code bellow, but its returning 395465626 everytime, I changed many things and Im still getting this answer, I cant figure out where the problem is, is it in the numbersWrittenByAbundant Array? or is it in the final for loop?

what this code does is
1) find all abundant numbers between 1 and 28123 and puts them in an array
2) subtract each abundant number from anther abundant number to find all the numbers that can be found by adding 2 abundant numbers and puts them in another array
3) loops from 1 to 28123 checking if each number is in the 2nd array (ie. can be written as a sum of 2 abundant numbers) if no adds it to the total of numbers

still im getting the wrong answer...
help please.
Peter Chase
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Joined: Oct 30, 2001
Posts: 1970


Well, for one thing, "counter" doesn't change in this loop, so you always write to the same element of abundantNumbers. I'm guessing you didn't want that.


Betty Rubble? Well, I would go with Betty... but I'd be thinking of Wilma.
Sam Benry
Ranch Hand

Joined: Mar 21, 2008
Posts: 89
ok I recoded it all
but Im still getting a wrong answer,
what the program does now:
get all abundant numbers until 28123 in an array
loops from zero till the last array index
in every loop it checks if the number is obtained by adding 2 abundant numbers, if its not, it adds it to the sum
it stops if the array index is reached or if the 28123 is reached (because all numbers above this can be obtained by adding 2 abundant numbers

whats wrong with the code? im getting a wrong answer
Joanne Neal
Rancher

Joined: Aug 05, 2005
Posts: 3720
    
  16
You're going to have to break this down. First thing to check is if the array of abundant numbers you are producing is correct. Assuming you know what numbers are supposed to be in there, print out all the values after you have created it to check you have created it correctly.
i.e. change your main method to
[ April 02, 2008: Message edited by: Joanne Neal ]

Joanne
Sam Benry
Ranch Hand

Joined: Mar 21, 2008
Posts: 89
yes i did that, the error is in getUnAbundantSumNumbers in the big nested loop somewhere...
but I dont know what is the error, because for small numbers (I tested 25) the result is correct, but when I put larges numbers (28123) the result is wrong :S
donno why...
Sam Benry
Ranch Hand

Joined: Mar 21, 2008
Posts: 89
found my mistake and found the solution from another place, but I still could not mange to fix the code, I still need help
the problem is when i=0 and j=4 the
counter is 36 and is adding all the number under a[i] + a[j] >> 12 + 30 = 42
but a[1]+a[2] >> 18 + 20 = 38 is less than 42
the compiler does not notice this and would include 38 as a number that cant be obtained by adding 2 numbers
I tried looping over all the numbers I got after I got them and check if suck mistaken numbers are included but the loop is so long it would not stop...
what do you think I should do?

this is the loop that should correct the problem, but it never ends

where all numbers are all numbers that we cant get by adding 2 abundant numbers and incrimental is the final value in the array that has a value...
 
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subject: Abundant Numbers