A= The square of the sum of the number of divisors of each of the divisors of n.

B= The sum of the cubes of the number of divisors of each of the divisors of n

Prove A=B

For example, let's have n=6. Its divisors are 1, 2, 3, and 6. These numbers respectively have 1, 2, 2, and 4 divisors. So A=(1+2+2+4)²=81 and B=1³+2³+2³+4³= 81.

You would win that bet. I used that and the Unique Factorization Theorem to solve the problem. The only thing is that the proof is loaded with superscripts and subscripts. Here would be a nice place for the comments section to allow HTML tags.

Posted by Bractals on 2006-07-22 09:39:17