Data commit

Task/Tau-function/Free-Pascal/tau-function.pas

@@ -0,0 +1,56 @@
+program Tau_function;
+{$IFDEF Windows}  {$APPTYPE CONSOLE} {$ENDIF}
+  function CountDivisors(n: NativeUint): integer;
+  var
+    q, p, cnt, divcnt: NativeUint;
+  begin
+    divCnt := 1;
+    if n > 1 then
+    begin
+      cnt := 1;
+      while not (Odd(n)) do
+      begin
+        n := n shr 1;
+        divCnt := divCnt+cnt;
+      end;
+      p := 3;
+      while p * p <= n do
+      begin
+        cnt := divCnt;
+        q := n div p;
+        while q * p = n do
+        begin
+          n := q;
+          q := n div p;
+          divCnt := divCnt+cnt;
+        end;
+        Inc(p, 2);
+      end;
+      if n <> 1 then
+        divCnt := divCnt+divCnt;
+    end;
+    CountDivisors := divCnt;
+  end;
+
+const
+  UPPERLIMIT = 99;
+  colWidth = trunc(ln(UPPERLIMIT)/ln(10))+1;
+var
+  i: NativeUint;
+begin
+  writeln('The tau functions for the first ',UPPERLIMIT,' positive integers are:');
+  Write('': colWidth+1);
+  for i := 0 to 9 do
+    Write(i: colWidth, ' ');
+  for i := 0 to UPPERLIMIT do
+  begin
+    if i mod 10 = 0 then
+    begin
+      writeln;
+      Write(i div 10: colWidth, '|');
+    end;
+    Write(CountDivisors(i): colWidth, ' ');
+  end;
+  writeln;
+  {$Ifdef Windows}readln;{$ENDIF}
+end.