Determine all possible positive whole numbers t such that t is equal to the sum of the squares of its four smallest positive divisors including 1.

For example, 1, 2, 4 and 5 are the four smallest positive divisors of 40.
But, 1² + 2² + 4²+ 5² = 46. So, t = 40 is NOT a valid solution.

(In reply to Sum thoughts by Leming)

I think I see what I missed.

I had developed the following in a spreadsheet and wondered about the direction of the problem; it seemed like the solutions were infinite:

1, 2, 3, 14 Result 210
1, 2, 6, 41 Result 1722
1, 2, 7, 18 Result 378
1, 3, 5, 35 Result 1260
1, 5, 7, 25 Result 700

In each of these I can find a lesser divisor than the double digit ones which voids my observation.


1, 2, 5, 10 Result 130   This did appear in my spreadsheet

Edited on May 3, 2007, 8:19 pm

Posted by brianjn on 2007-05-03 20:07:00