I need help in Maxima (a "simple" problem [how is the syntax for the formula])

   From: "Robert BIGDOWSKI" <robert.bigdowski at dudelange.lu>
   
   a, b, n natural numbers > 0
   a+b <= x
   how many solutions f(x) exists
   with { a+b | a * b }, ie a*b = (a+b) * n
   
   as a starter. Has anyone an idea how to start - browsing through the
   documentation of maxima did't give me an idea.

You don't state whether you want a closed-form solution or a
computational procedure.  The latter is easily achieved in almost any
ceneral-purpose computer language, and since Maxima provides escape to
Common Lisp, writing a simple function in Common Lisp would be one way
to start.  In Common Lisp:

(defun f (x)
  (loop for a from 1 below x
      sum (loop for b from 1 upto (- x a)
	      when (= 0 (mod (* a b) (+ a b)))
	      count 1)))

This solution has O^2 behavior, but is tolerably fast enough to solve
(f 100000) in less than a minute on a fast computer.