Problem Statement

The factorial of a number, written as

n !

{\displaystyle n!}

, is defined as

n !

n ( n − 1 ) ( n − 2 ) . . . ( 2 ) ( 1 )

{\displaystyle n!=n(n-1)(n-2)...(2)(1)}

. Multifactorials generalize factorials as follows: In all cases, the terms in the products are positive integers. If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:

Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.

Let's start with the solution:

(defun mfac (n m)
  (reduce #'* (loop for i from n downto 1 by m collect i)))

(loop for i from 1 to 10
      do (format t "~2@a: ~{~a~^ ~}~%"
                 i (loop for j from 1 to 10
                         collect (mfac j i))))