anchor.diff:  (defun euler-71 ()
     (numerator (euler-problem-71 (expt 10 6) 3/7)))
   
  -;;; for 72 i think i can use the toitent function once it is fixed up
  +(defun euler-problem-72 (ceiling-value)
  +  (loop for denominator from 2 to ceiling-value
  +       summing (euler-toitent-function denominator)))
  +
  +(defun euler-72 ()
  +  (euler-problem-72 (expt 10 6)))
   
   (defun euler-problem-73 (max-denominator lower-fence upper-fence)
     (loop for denom from 1 to max-denominator
  
positive.code:         with ratio = 0
          as toitent = (euler-toitent-function i)
          as cur-ratio = (/ i toitent)
          do (format t "~&~a ~a ~a" i toitent cur-ratio)
          when (> cur-ratio ratio)
            do (setf max-i i
                     ratio cur-ratio)
          finally (return max-i)))
  
  (defun euler-problem-71 (max-denominator target-fraction)
    (loop for denom from 1 to max-denominator
  
negative.code:                                            (factorial (digit-char-p digit-char)))))
  
  
  (defun digit-factorial-chain (val)
    (loop
      with cur-val = (digit-factorial val)
      if (or (= cur-val val) (member cur-val chain :test #'=))
        return (values (1+ chain-length) (cons val chain) cur-val)
      else collect cur-val into chain
           and count 1 into chain-length
           and do (setf cur-val (digit-factorial cur-val))))
  
  (defun euler-problem-74 (ceiling-value)
    (time (loop for i from 1 to ceiling-value
                as chain-length = (digit-factorial-chain i)
              when (= chain-length 60)
                count 1 into long-chain-count
                finally (return long-chain-count))))
  
  (defun euler-74 ()
    (euler-problem-74 (expt 10 6)))
  