ocaml: phase 5.1 abundant.ml baseline (count abundant numbers < 100 = 21)

A number n is abundant if its proper-divisor sum exceeds n. Reuses
the trial-division div_sum helper:

  let count_abundant n =
    let c = ref 0 in
    for i = 12 to n - 1 do
      if div_sum i > i then c := !c + 1
    done;
    !c

  count_abundant 100 = 21

Abundant numbers under 100, starting at 12, 18, 20, 24, 30, 36, 40,
42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96 -> 21.

Companion to euler21_small.ml (amicable). The classification:
  perfect:  d(n) = n   (e.g. 6, 28)
  abundant: d(n) > n   (e.g. 12, 18)
  deficient:d(n) < n   (everything else)

124 baseline programs total.

lib/ocaml/baseline/abundant.ml

@@ -0,0 +1,23 @@
+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 count_abundant n =
+  let c = ref 0 in
+  for i = 12 to n - 1 do
+    if div_sum i > i then c := !c + 1
+  done;
+  !c
+
+;;
+
+count_abundant 100

lib/ocaml/baseline/expected.json

@@ -1,4 +1,5 @@
 {
+  "abundant.ml": 21,
   "ackermann.ml": 125,
   "adler32.ml": 300286872,
   "anagram_check.ml": 2,