From 1f09714d469bd8f7ea832c4bdbb357a6f7b9d34c Mon Sep 17 00:00:00 2001
From: felixm <mail@felixm.de>
Date: Sat, 20 Apr 2024 15:19:37 -0400
Subject: [PATCH] Solve problem 203.

---
 python/e203.py | 55 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 55 insertions(+)
 create mode 100644 python/e203.py

diff --git a/python/e203.py b/python/e203.py
new file mode 100644
index 0000000..e28513e
--- /dev/null
+++ b/python/e203.py
@@ -0,0 +1,55 @@
+from lib_prime import primes
+from math import sqrt
+
+
+def pascal_numbers_till(row):
+    def pascal_next(xs):
+        r = [xs[0]]
+        for i in range(len(xs) - 1):
+            r.append(xs[i] + xs[i + 1])
+        r.append(xs[-1])
+        return r
+
+    all = set([1])
+    xs = [1]
+    for _ in range(row - 1):
+        xs = pascal_next(xs)
+        all |= set(xs)
+    return sorted(list(set(all)))
+
+
+def is_square_free(ps, n):
+    for p in ps:
+        if n % p == 0:
+            return False
+    return True
+
+
+def solve(n):
+    r = 0
+    pascals = pascal_numbers_till(n)
+    ps = [p * p for p in primes(int(sqrt(max(pascals))))]
+    for n in pascals:
+        if is_square_free(ps, n):
+            r += n
+    return r
+
+
+def test():
+    assert pascal_numbers_till(1) == [1]
+    assert pascal_numbers_till(2) == [1]
+    assert pascal_numbers_till(3) == [1, 2]
+    assert pascal_numbers_till(8) == [1, 2, 3, 4, 5, 6, 7, 10, 15, 20, 21, 35]
+    assert solve(8) == 105
+
+
+def euler_203():
+    test()
+    return solve(51)
+
+
+if __name__ == "__main__":
+    solution = euler_203()
+    print("e203.py: " + str(solution))
+    assert solution == 34029210557338
+