Solved 68 and rewrote 69 in Python.

python/e069.py

@@ -1,62 +1,23 @@
+from lib_prime import primes
+from lib_misc import gcd
 
 
-def prime_factors(n):
-    f = []
-    while n % 2 == 0:
-        f.append(2)
-        n //= 2
-    d = 3
-    while d * d <= n:
-        while n % d == 0:
-            f.append(d)
-            n //= d
-        d += 2
-    if n != 1:
-        f.append(n)
-    return f
-
-assert(prime_factors(8) == [2, 2, 2])
-assert(prime_factors(2501232) == [2, 2, 2, 2, 3, 107, 487])
-
-
-def prime_factors_unique(n):
-    f = []
-    if n % 2 == 0:
-        f.append(2)
-    while n % 2 == 0:
-        n //= 2
-    d = 3
-    while d * d <= n:
-        if n % d == 0:
-            f.append(d)
-        while n % d == 0:
-            n //= d
-        d += 2
-    if n != 1:
-        f.append(n)
-    return f
-
-
-def prime_factors_count(n):
-    return len(prime_factors_unique(n))
-
-
-print(prime_factors_count(9699690))
-
-#factor_count_max = 0
-#n_max = 0
-#for n in range(1, 1000001):
-#    factor_count = prime_factors_count(n)
-#    if factor_count > factor_count_max:
-#        factor_count_max = factor_count
-#        n_max = n
-#print("factor count: {} n: {}".format(factor_count_max, n_max))
+def relative_primes_count(n):
+    return len([i for i in range(1, n) if gcd(n, i) == 1])
 
 
 def get_phi(n):
-    phi = n
-    for p in prime_factors_unique(n):
-        phi *= (1 - 1 / p)
-    return int(phi)
+    return n / relative_primes_count(n)
 
-print(get_phi(210412312))
+
+def euler_069():
+    s = 1
+    for p in primes(1000):
+        s *= p
+        if s > 1000000:
+            return s // p
+
+
+if __name__ == "__main__":
+    print("e069.py: " + str(euler_069()))
+    assert(euler_069() == 510510)