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.

It looks correct to me now.  I do intend to do a further verification (what I would term an acid test) by specializing to n=(2^3)*(3^2) and working out each step numercially. I would urge others to try the same.

Posted by Richard on 2006-07-23 04:00:33