Weird numbers

maths/weird_number.py

@@ -0,0 +1,101 @@
+"""
+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.")