ocaml: phase 5.1 harshad.ml baseline (count Niven/Harshad numbers <= 100 = 33)

A Harshad (or Niven) number is divisible by its digit sum:

  let count_harshad limit =
    let c = ref 0 in
    for n = 1 to limit do
      if n mod (digit_sum n) = 0 then c := !c + 1
    done;
    !c

  count_harshad 100 = 33

All single-digit numbers (1..9) qualify trivially. Plus 10, 12, 18,
20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80,
81, 84, 90, 100 (24 more) = 33 total under 100.

133 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -59,6 +59,7 @@
   "grid_paths.ml": 210,
   "group_consec.ml": 53,
   "hailstone.ml": 111,
+  "harshad.ml": 33,
   "hamming.ml": 4,
   "hanoi.ml": 1023,
   "hist.ml": 75,

lib/ocaml/baseline/harshad.ml

@@ -0,0 +1,19 @@
+let digit_sum n =
+  let m = ref n in
+  let s = ref 0 in
+  while !m > 0 do
+    s := !s + !m mod 10;
+    m := !m / 10
+  done;
+  !s
+
+let count_harshad limit =
+  let c = ref 0 in
+  for n = 1 to limit do
+    if n mod (digit_sum n) = 0 then c := !c + 1
+  done;
+  !c
+
+;;
+
+count_harshad 100

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-10 Phase 5.1 — harshad.ml baseline (count Niven/Harshad
+  numbers ≤ 100 = 33). A Harshad number is divisible by its digit
+  sum. All single-digit numbers qualify trivially (9). Plus 10, 12,
+  18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70,
+  72, 80, 81, 84, 90, 100 (24 more) = 33 under 100. 133 baseline
+  programs total.
 - 2026-05-10 Phase 5.1 — reverse_int.ml baseline (digit-reverse,
   reverse(12345) + reverse(100) + reverse(7) = 54321 + 1 + 7 =
   54329). Walks digits via mod 10 / div 10, accumulating the