Initial data commit

Task/Tau-function/Swift/tau-function.swift

@@ -0,0 +1,37 @@
+import Foundation
+
+// See https://en.wikipedia.org/wiki/Divisor_function
+func divisorCount(number: Int) -> Int {
+    var n = number
+    var total = 1
+    // Deal with powers of 2 first
+    while (n & 1) == 0 {
+        total += 1
+        n >>= 1
+    }
+    // Odd prime factors up to the square root
+    var p = 3
+    while p * p <= n {
+        var count = 1
+        while n % p == 0 {
+            count += 1
+            n /= p
+        }
+        total *= count
+        p += 2
+    }
+    // If n > 1 then it's prime
+    if n > 1 {
+        total *= 2
+    }
+    return total
+}
+
+let limit = 100
+print("Count of divisors for the first \(limit) positive integers:")
+for n in 1...limit {
+    print(String(format: "%3d", divisorCount(number: n)), terminator: "")
+    if n % 20 == 0 {
+        print()
+    }
+}