ocaml: phase 5.1 triangle_div.ml baseline (first triangle with >10 divisors = 120)

PE12 with target = 10:

  let count_divisors n =
    let c = ref 0 in
    let i = ref 1 in
    while !i * !i <= n do
      if n mod !i = 0 then begin
        c := !c + 1;
        if !i * !i <> n then c := !c + 1
      end;
      i := !i + 1
    done;
    !c

  let first_triangle_with_divs target =
    walk triangles T(n) = T(n-1) + n until count_divisors T > target

T(15) = 120 has 16 divisors — first to exceed 10. Real PE12 uses
target 500 (answer 76576500); 10 stays well under budget.

126 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -122,6 +122,7 @@
   "sum_squares.ml": 385,
   "tree_depth.ml": 4,
   "triangle.ml": 11,
+  "triangle_div.ml": 120,
   "twosum.ml": 5,
   "unique_set.ml": 9,
   "validate.ml": 417,

lib/ocaml/baseline/triangle_div.ml

@@ -0,0 +1,26 @@
+let count_divisors n =
+  let c = ref 0 in
+  let i = ref 1 in
+  while !i * !i <= n do
+    if n mod !i = 0 then begin
+      c := !c + 1;
+      if !i * !i <> n then c := !c + 1
+    end;
+    i := !i + 1
+  done;
+  !c
+
+let first_triangle_with_divs target =
+  let t = ref 0 in
+  let n = ref 0 in
+  let found = ref false in
+  while not !found do
+    n := !n + 1;
+    t := !t + !n;
+    if count_divisors !t > target then found := true
+  done;
+  !t
+
+;;
+
+first_triangle_with_divs 10

plans/ocaml-on-sx.md

@@ -407,6 +407,11 @@ _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 — triangle_div.ml baseline (first triangle
+  number with > 10 divisors = 120). PE12 with target 10. T(15) = 120
+  has 16 divisors {1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120} —
+  first to break 10. Real PE12 uses target 500 (answer 76576500);
+  10 stays well under our budget. 126 baseline programs total.
 - 2026-05-10 Phase 5.1 — perfect.ml baseline (count perfect numbers
   ≤ 500 = 3). Perfect numbers = those where d(n) = n. Three under
   500: 6, 28, 496. (8128 is the next.) Same div_sum machinery as