problem 12 in julia

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+###
+# Highly divisible triangular number
+# Problem 12
+#
+# The sequence of triangle numbers is generated by adding the natural numbers. So the 7th
+# triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
+# 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
+# Let us list the factors of the first seven triangle numbers:
+#  1: 1 3: 1,3 6: 1,2,3,610: 1,2,5,1015: 1,3,5,1521: 1,3,7,2128: 1,2,4,7,14,28
+# We can see that 28 is the first triangle number to have over five divisors.
+# What is the value of the first triangle number to have over five hundred divisors?
+###
+
+
+using Base.Iterators
+
+
+# Eddie woo factors: https://www.youtube.com/watch?v=KRfv9pQCTDE
+#
+# we can skip the numbers after the square root since factors
+# come in pairs reflected at the square root
+# e.g: 24: 1, 2, 3, 4, 6, 8, 12, 24
+#      1 - 24
+#      2 - 12
+#      3 - 8
+#      4 - 6
+#
+# all non prime numbers have an even number of factors except for the squares
+# since they have a "pair" that is the same number
+# e.g 16: 1, 2, 4, 8, 16
+#     1 - 16
+#     2 - 8
+#     4 - 4 <<<
+#
+# square numbers (i.e 4, 9, 16, 25, etc) have 3 divisors unless their root is also a square number
+# 4: 1, 2, 4 (2 is prime)
+# 9: 1, 3, 9 (3 is prime)
+# 16: 1, 2, 4, 8, 16 (4 is square)
+
+function divisor_count(n)
+    count = 0
+    s = 0
+    while true
+        s = floor(Integer, √n)
+        (n != 1 && s * s == n) || break
+        count += 1
+        n = s
+    end
+    for d in 1:s
+        if n % d == 0
+            count += 2
+        end
+    end
+    return count
+end
+
+total = 0
+for n in countfrom(1)
+    global total += n
+    if divisor_count(total) > 500
+        println(total)
+        break
+    end
+end
+
+# can't do  countfrom |> cumsum |> takewhile |> last because cumsum doesn't support infinite iterators