ocaml: phase 5.1 euler21_small.ml baseline (sum of amicable numbers <= 300 = 504)

div_sum computes proper divisor sum via trial division up to sqrt(n):

  let div_sum n =
    let s = ref 1 in
    let i = ref 2 in
    while !i * !i <= n do
      if n mod !i = 0 then begin
        s := !s + !i;
        let q = n / !i in
        if q <> !i then s := !s + q
      end;
      i := !i + 1
    done;
    if n = 1 then 0 else !s

Outer loop finds amicable pairs (a, b) with d(a) = b, d(b) = a,
a != b. Only pair under 300 is (220, 284); 220 + 284 = 504.

Real PE21 uses 10000 (answer 31626). 300 keeps the run under
budget while exercising the same divisor-sum trick.

119 baseline programs total.

lib/ocaml/baseline/euler21_small.ml

@@ -0,0 +1,25 @@
+let div_sum n =
+  let s = ref 1 in
+  let i = ref 2 in
+  while !i * !i <= n do
+    if n mod !i = 0 then begin
+      s := !s + !i;
+      let q = n / !i in
+      if q <> !i then s := !s + q
+    end;
+    i := !i + 1
+  done;
+  if n = 1 then 0 else !s
+
+let euler21 limit =
+  let total = ref 0 in
+  for a = 2 to limit do
+    let b = div_sum a in
+    if b <> a && b > a && b <= limit && div_sum b = a then
+      total := !total + a + b
+  done;
+  !total
+
+;;
+
+euler21 300

lib/ocaml/baseline/expected.json

@@ -30,6 +30,7 @@
   "euler10.ml": 1060,
   "euler14.ml": 97,
   "euler2.ml": 4613732,
+  "euler21_small.ml": 504,
   "euler25.ml": 55,
   "euler28.ml": 261,
   "euler30_cube.ml": 1301,

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.
+- 2026-05-09 Phase 5.1 — euler21_small.ml baseline (sum of amicable
+  numbers ≤ 300 = 504). div_sum computes proper divisor sum via
+  trial division up to √n; outer loop finds amicable pairs (a, b)
+  with d(a) = b, d(b) = a, a ≠ b. Only pair under 300 is (220, 284).
+  Real PE21 uses 10000 (answer 31626). 119 baseline programs total.
 - 2026-05-09 Phase 5.1 — euler30_cube.ml baseline (sum of numbers
   equal to sum of cubes of their digits, ≤999 = 1301). The full
   numbers are 153 + 370 + 371 + 407 = 1301. PE30 proper uses 5th