Update algo. for MPAS possible MPAS partition cores

The old algorithm wasn't generating the breadth of parition
sizes that the E3SM team needs.  The updated algorithm seems
likely to generate nearly all of the partition sizes that
could conceivable be useful for a given mesh.

compass/ocean/tests/global_ocean/files_for_e3sm/graph_partition.py

@@ -1,7 +1,7 @@
 import numpy as np
 
 
-def get_core_list(ncells, max_cells_per_core=6000, min_cells_per_core=100):
+def get_core_list(ncells, max_cells_per_core=30000, min_cells_per_core=2):
     """
     Get a fairly exhaustive list of core counts to partition a given number of
     cells into
@@ -26,15 +26,36 @@ def get_core_list(ncells, max_cells_per_core=6000, min_cells_per_core=100):
     """
     min_graph_size = int(ncells / max_cells_per_core)
     max_graph_size = int(ncells / min_cells_per_core)
-    n_power2 = 2**np.arange(1, 21)
-    n_multiples12 = 12 * np.arange(1, 9)
 
-    cores = n_power2
-    for power10 in range(3):
-        cores = np.concatenate([cores, 10**power10 * n_multiples12])
-
-    mask = np.logical_and(cores >= min_graph_size,
-                          cores <= max_graph_size)
-    cores = cores[mask]
-
-    return cores
+    print(min_graph_size, max_graph_size)
+
+    cores = []
+    for candidate in range(min_graph_size, max_graph_size):
+        factors = _prime_factors(candidate)
+        twos = np.count_nonzero(factors == 2)
+        fives = np.count_nonzero(factors == 5)
+        gt_five = np.count_nonzero(factors > 5)
+        big_factor = factors.max()
+        if twos > 0 and fives <= twos and gt_five <= 1 and big_factor <= 7:
+            cores.append(candidate)
+        # small odd powers of 3 and a few that correspond to divisors of the
+        # ne30 (30x30x6=5400) size
+        elif candidate in [3, 9, 15, 21, 225, 675, 1350]:
+            cores.append(candidate)
+
+    return np.array(cores)
+
+
+# https://stackoverflow.com/a/22808285
+def _prime_factors(n):
+    i = 2
+    factors = []
+    while i * i <= n:
+        if n % i:
+            i += 1
+        else:
+            n //= i
+            factors.append(i)
+    if n > 1:
+        factors.append(n)
+    return np.array(factors)