Data update

Task/Tau-function/Asymptote/tau-function.asymptote

@@ -0,0 +1,14 @@
+write("The tau functions for the first 100 positive integers are:");
+for (int N = 1; N <= 100; ++N) {
+    int T;
+    if (N < 3) {
+        T = N;
+    } else {
+        T = 2;
+        for (int A = 2; A <= (N + 1) / 2; ++A) {
+            if (N % A == 0) T = T + 1;
+        }
+    }
+    write(format("%3d", T), suffix=none);
+    if (N % 10 == 0) write("");
+}

Task/Tau-function/Dart/tau-function.dart

@@ -0,0 +1,22 @@
+int divisorCount(int n) {
+  int total = 1;
+  // Deal with powers of 2 first
+  for (; (n & 1) == 0; n >>= 1) total++;
+  // Odd prime factors up to the square root
+  for (int p = 3; p * p <= n; p += 2) {
+    int count = 1;
+    for (; n % p == 0; n ~/= p) count++;
+    total *= count;
+  }
+  // If n > 1 then it's prime
+  if (n > 1) total *= 2;
+  return total;
+}
+
+void main() {
+  const int limit = 100;
+  print("Count of divisors for the first $limit positive integers:");
+  for (int n = 1; n <= limit; ++n) {
+    print(divisorCount(n).toString().padLeft(3));
+  }
+}