Determine all possible value(s) of a positive integer N that satisfies the following conditions:

(i) N is the product of three prime numbers, whose squares sum to 2331.

(ii) The sum of the positive divisors of N ( including 1 and N) is 10560.

There are several that satisfy condition 1:  8987, 10373, 11803, 13243, & 20677.  But the only of these that satisfies condition 2 is 8987.

 

8987 = 11 * 19 * 43

2331 = 11^2 + 19^2 + 43^2

10560 = 1 + 11 + 19 + 43 + 209 + 817 + 473 + 8987

Posted by hoodat on 2009-10-19 13:33:38