Data commit

Task/Aliquot-sequence-classifications/Python/aliquot-sequence-classifications.py

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+from proper_divisors import proper_divs
+from functools import lru_cache
+
+
+@lru_cache()
+def pdsum(n):
+    return sum(proper_divs(n))
+
+
+def aliquot(n, maxlen=16, maxterm=2**47):
+    if n == 0:
+        return 'terminating', [0]
+    s, slen, new = [n], 1, n
+    while slen <= maxlen and new < maxterm:
+        new = pdsum(s[-1])
+        if new in s:
+            if s[0] == new:
+                if slen == 1:
+                    return 'perfect', s
+                elif slen == 2:
+                    return 'amicable', s
+                else:
+                    return 'sociable of length %i' % slen, s
+            elif s[-1] == new:
+                return 'aspiring', s
+            else:
+                return 'cyclic back to %i' % new, s
+        elif new == 0:
+            return 'terminating', s + [0]
+        else:
+            s.append(new)
+            slen += 1
+    else:
+        return 'non-terminating', s
+
+if __name__ == '__main__':
+    for n in range(1, 11):
+        print('%s: %r' % aliquot(n))
+    print()
+    for n in [11, 12, 28, 496, 220, 1184,  12496, 1264460, 790, 909, 562, 1064, 1488, 15355717786080]:
+        print('%s: %r' % aliquot(n))