The Harshad or Niven numbers are positive integers ≥ 1 that are divisible by the sum of their digits.

For example,   42   is a Harshad number as   42   is divisible by   (4 + 2)   without remainder.

Assume that the series is defined as the numbers in increasing order.



Task

The task is to create a function/method/procedure to generate successive members of the Harshad sequence.

Use it to:

   list the first 20 members of the sequence,   and
   list the first Harshad number greater than 1000.


Show your output here.



Related task
   Increasing gaps between consecutive Niven numbers


See also
    OEIS: A005349


(defn digsum [n acc]
  (if (zero? n) acc
      (digsum (quot n 10) (+ acc (mod n 10)))))
 
(let [harshads (filter
                 #(zero? (mod % (digsum % 0)))
                 (iterate inc 1))]
  (prn (take 20 harshads))
  (prn (first (filter #(> % 1000) harshads))))