ocaml: phase 5.1 euler29_small.ml baseline (distinct a^b for 2<=a,b<=5 = 15)

Compute every power a^b for a, b in [2..N] and count distinct
values. Hashtbl as a set with unit-payload (iter-168 idiom):

  let euler29 n =
    let h = Hashtbl.create 64 in
    for a = 2 to n do
      for b = 2 to n do
        let p = ref 1 in
        for _ = 1 to b do p := !p * a done;
        Hashtbl.replace h !p ()
      done
    done;
    Hashtbl.length h

For N=5: 16 powers minus one duplicate (4^2 = 2^4 = 16) -> 15.

Real PE29 uses N=100 (answer 9183).

120 baseline programs total — milestone.

lib/ocaml/baseline/euler29_small.ml

@@ -0,0 +1,14 @@
+let euler29 n =
+  let h = Hashtbl.create 64 in
+  for a = 2 to n do
+    for b = 2 to n do
+      let p = ref 1 in
+      for _ = 1 to b do p := !p * a done;
+      Hashtbl.replace h !p ()
+    done
+  done;
+  Hashtbl.length h
+
+;;
+
+euler29 5

lib/ocaml/baseline/expected.json

@@ -33,6 +33,7 @@
   "euler21_small.ml": 504,
   "euler25.ml": 55,
   "euler28.ml": 261,
+  "euler29_small.ml": 15,
   "euler30_cube.ml": 1301,
   "euler3.ml": 29,
   "euler4_small.ml": 9009,

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 — euler29_small.ml baseline (distinct a^b for
+  2≤a,b≤5 = 15). 16 powers minus the one duplicate (4^2 = 2^4 = 16)
+  → 15 distinct values. Hashtbl as a set with unit-payload (the
+  iter-168 idiom). Real PE29 uses N=100 (answer 9183). 120 baseline
+  programs total — milestone.
 - 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)