Initial data commit

Task/Legendre-prime-counting-function/Python/legendre-prime-counting-function.py

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+from primesieve import primes
+from math import isqrt
+from functools import cache
+
+p = primes(isqrt(1_000_000_000))
+
+@cache
+def phi(x, a):
+    res = 0
+    while True:
+        if not a or not x:
+            return x + res
+
+        a -= 1
+        res -= phi(x//p[a], a) # partial tail recursion
+
+def legpi(n):
+    if n < 2: return 0
+
+    a = legpi(isqrt(n))
+    return phi(n, a) + a - 1
+
+for e in range(10):
+    print(f'10^{e}', legpi(10**e))