Data commit

Task/Chowla-numbers/Python/chowla-numbers-1.py

@@ -0,0 +1,32 @@
+# https://docs.sympy.org/latest/modules/ntheory.html#sympy.ntheory.factor_.divisors
+from sympy import divisors
+
+def chowla(n):
+    return 0 if n < 2 else sum(divisors(n, generator=True)) - 1 -n
+
+def is_prime(n):
+    return chowla(n) == 0
+
+def primes_to(n):
+    return sum(chowla(i) == 0 for i in range(2, n))
+
+def perfect_between(n, m):
+    c = 0
+    print(f"\nPerfect numbers between [{n:_}, {m:_})")
+    for i in range(n, m):
+        if i > 1 and chowla(i) == i - 1:
+            print(f"  {i:_}")
+            c += 1
+    print(f"Found {c} Perfect numbers between [{n:_}, {m:_})")
+
+
+if __name__ == '__main__':
+    for i in range(1, 38):
+        print(f"chowla({i:2}) == {chowla(i)}")
+    for i in range(2, 6):
+        print(f"primes_to({10**i:_}) == {primes_to(10**i):_}")
+    perfect_between(1, 1_000_000)
+    print()
+    for i in range(6, 8):
+        print(f"primes_to({10**i:_}) == {primes_to(10**i):_}")
+    perfect_between(1_000_000, 35_000_000)

Task/Chowla-numbers/Python/chowla-numbers-2.py

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+from numba import jit
+
+# https://docs.sympy.org/latest/modules/ntheory.html#sympy.ntheory.factor_.divisors
+from sympy import divisors
+
+@jit
+def chowla(n):
+    return 0 if n < 2 else sum(divisors(n, generator=True)) - 1 -n
+
+@jit
+def is_prime(n):
+    return chowla(n) == 0
+
+@jit
+def primes_to(n):
+    acc = 0
+    for i in range(2, n):
+        if chowla(i) == 0:
+            acc += 1
+    return acc
+
+@jit
+def _perfect_between(n, m):
+    for i in range(n, m):
+        if i > 1 and chowla(i) == i - 1:
+            yield i
+
+def perfect_between(n, m):
+    c = 0
+    print(f"\nPerfect numbers between [{n:_}, {m:_})")
+    for i in _perfect_between(n, m):
+        print(f"  {i:_}")
+        c += 1
+    print(f"Found {c} Perfect numbers between [{n:_}, {m:_})")