Perfect numbers less than 10 000

Question

Im trying to find perfect numbers less that 10 000. I was told that the best way to do this is by using maple, but I don't know how to use latex except the basics like graphing. Can someone help me do this in maple? thanks.

I'm not sure in Maple, but in GAP they can be found using Filtered([1..9999],i->Sum(DivisorsInt(i))=2*i); which returns [ 6, 28, 496, 8128 ]. It's just brute force computation; nothing intelligent. — Douglas S. Stones, Oct 11 '13 at 20:17
You can look in OEIS Are you aware of the link (for even ones, the only ones known to exist) to the Mersenne primes? — Ross Millikan, Oct 11 '13 at 20:19
@DonAntonio I didn't know $1$ was a perfect number. How do you define "perfect number"? — bof, Oct 11 '13 at 20:48
@bof, 1 is not a perfect number (according to most sources). A more exact definition is a perfect number is one such that the sum of its divisors (including itself) equals two times itself. — MT_, Oct 11 '13 at 21:15
Perfect number = one which equals the sum of its proper divisors... or $;1;$. Just kidding: take out $;1;$ , we won't weep for that, @bof . — DonAntonio, Oct 11 '13 at 23:03
The Euclid-Euler theorem states that an even number is perfect if and only if it is of the form $2^{k-1}(2^k-1)$. There are no known odd perfect numbers, and folks have looked well beyond $10000$ for them. — MartianInvader, Oct 11 '13 at 23:41
Does this answer your question? find the largest perfect number less than $10,000$ in Maple — JRN, Jul 24 '22 at 02:28

score 1 · Accepted Answer · edited Oct 11 '13 at 23:25

1

You can find much in wiki (http://en.wikipedia.org/wiki/Perfect_number):

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself.

And Douglas ist right. Check http://en.wikipedia.org/wiki/List_of_perfect_numbers

Hope that helps.

You don't need to use maple. You can use c. Try this code (I very quickly wrote it)

int main() {
  int n, i, sum;

  for (n=0; n<10000; n++) {
    i=1;
    sum=0;

    while (i<n) {
      if (n%i == 0)
        sum = sum+i;
      i++;
    }
    if (sum == n)
      printf("%d\n", i);
  }
  return 0;
}

Output is

Hope that helps.

edited Oct 11 '13 at 23:25

MJD

65,394
39
298
580

answered Oct 11 '13 at 20:57

Umberto

1,263
8
16

Thanks a lot! But If want to do it in maple? The same code would work? Can you help me find a code for this so that it works in maple? thanks – Oct 11 '13 at 21:25
I don't have maple so cannot check directly, but it seems that here you can find some information: http://www.mapleprimes.com/questions/41246-Perfect-Numbers but it seems that Maple does not have a direct function to find the perfect numbers. You will have to write some kind of code. – Umberto Oct 11 '13 at 21:27
See comments above on 1 being a perfect number. – JRN Oct 12 '13 at 00:11

score 0 · Answer 2 · answered Oct 13 '13 at 01:23

In Maple,

seq(`if`(`+`(numtheory:-divisors(i)[])=2*i,i,NULL),i=1..9999);

                    6, 28, 496, 8128

Or, if you accept some background theory as given,

restart:

i:=1:
k:=numtheory:-mersenne([i]):
T:=k*((k+1)/2):
L:=[]:
while T < 10000 do
   L:=[L[],T];
   i:=i+1;
   k:=numtheory:-mersenne([i]);
   T:=k*((k+1)/2);
end do:
L;

                   [6, 28, 496, 8128]

Perfect numbers less than 10 000

2 Answers2