Weird numbers (#6871)

* Create weird_number.py

In number theory, a weird number is a natural number that is abundant but not semiperfect

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* Update weird_number.py

* Update weird_number.py

* Update weird_number.py

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

maths/weird_number.py

@@ -0,0 +1,100 @@
+"""
+https://en.wikipedia.org/wiki/Weird_number
+
+Fun fact: The set of weird numbers has positive asymptotic density.
+"""
+from math import sqrt
+
+
+def factors(number: int) -> list[int]:
+    """
+    >>> factors(12)
+    [1, 2, 3, 4, 6]
+    >>> factors(1)
+    [1]
+    >>> factors(100)
+    [1, 2, 4, 5, 10, 20, 25, 50]
+
+    # >>> factors(-12)
+    # [1, 2, 3, 4, 6]
+    """
+
+    values = [1]
+    for i in range(2, int(sqrt(number)) + 1, 1):
+        if number % i == 0:
+            values.append(i)
+            if int(number // i) != i:
+                values.append(int(number // i))
+    return sorted(values)
+
+
+def abundant(n: int) -> bool:
+    """
+    >>> abundant(0)
+    True
+    >>> abundant(1)
+    False
+    >>> abundant(12)
+    True
+    >>> abundant(13)
+    False
+    >>> abundant(20)
+    True
+
+    # >>> abundant(-12)
+    # True
+    """
+    return sum(factors(n)) > n
+
+
+def semi_perfect(number: int) -> bool:
+    """
+    >>> semi_perfect(0)
+    True
+    >>> semi_perfect(1)
+    True
+    >>> semi_perfect(12)
+    True
+    >>> semi_perfect(13)
+    False
+
+    # >>> semi_perfect(-12)
+    # True
+    """
+    values = factors(number)
+    r = len(values)
+    subset = [[0 for i in range(number + 1)] for j in range(r + 1)]
+    for i in range(r + 1):
+        subset[i][0] = True
+
+    for i in range(1, number + 1):
+        subset[0][i] = False
+
+    for i in range(1, r + 1):
+        for j in range(1, number + 1):
+            if j < values[i - 1]:
+                subset[i][j] = subset[i - 1][j]
+            else:
+                subset[i][j] = subset[i - 1][j] or subset[i - 1][j - values[i - 1]]
+
+    return subset[r][number] != 0
+
+
+def weird(number: int) -> bool:
+    """
+    >>> weird(0)
+    False
+    >>> weird(70)
+    True
+    >>> weird(77)
+    False
+    """
+    return abundant(number) and not semi_perfect(number)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod(verbose=True)
+    for number in (69, 70, 71):
+        print(f"{number} is {'' if weird(number) else 'not '}weird.")