Data update

Task/Totient-function/Lua/totient-function-2.lua

@@ -0,0 +1,44 @@
+do
+    function totient( n ) -- returns the number of integers k where 1 <= k <= n that are mutually prime to n
+        if     n <  3 then return 1
+        elseif n == 3 then return 2
+        else
+           local result, v, i = n, n, 2
+           while i * i <= v do
+               if v % i == 0 then
+                   while v % i == 0 do v = math.floor( v / i ) end
+                   result = result - math.floor( result / i )
+               end
+               if i == 2 then
+                   i = 1
+               end
+               i = i + 2
+           end
+           if v > 1 then result = result - math.floor( result / v ) end
+           return result
+       end
+    end
+    -- show the totient function values for the first 25 integers
+    io.write( " n  phi(n) remarks\n" )
+    for n = 1,25 do
+        local tn = totient( n )
+        io.write( string.format( "%2d", n ), ": ", string.format( "%5d", tn )
+                , ( tn == n - 1 and tn ~= 0 and "  n is prime" or "" )
+                , "\n"
+                )
+    end
+    -- use the totient function to count primes
+    local n100, n1000, n10000, n100000 = 0, 0, 0, 0
+    for n = 1,100000 do
+        if totient( n ) == n - 1 then
+            if n <=    100 then    n100 = n100    + 1 end
+            if n <=   1000 then   n1000 = n1000   + 1 end
+            if n <=  10000 then  n10000 = n10000  + 1 end
+            if n <= 100000 then n100000 = n100000 + 1 end
+        end
+    end
+    io.write( "There are ", string.format( "%6d",    n100 ), " primes below      100\n" )
+    io.write( "There are ", string.format( "%6d",   n1000 ), " primes below    1 000\n" )
+    io.write( "There are ", string.format( "%6d",  n10000 ), " primes below   10 000\n" )
+    io.write( "There are ", string.format( "%6d", n100000 ), " primes below  100 000\n" )
+end