Data update

Task/Totient-function/ALGOL-68/totient-function.alg

@@ -24,7 +24,10 @@ BEGIN
     print( ( " n  phi(n) remarks", newline ) );
     FOR n TO 25 DO
         INT tn = totient( n );
-        print( ( whole( n, -2 ), ": ", whole( tn, -5 ), IF tn = n - 1 AND tn /= 0 THEN "  n is prime" ELSE "" FI, newline ) )
+        print( ( whole( n, -2 ), ": ", whole( tn, -5 )
+               , IF tn = n - 1 AND tn /= 0 THEN "  n is prime" ELSE "" FI, newline
+               )
+             )
     OD;
     # use the totient function to count primes #
     INT n100 := 0, n1000 := 0, n10000 := 0, n100000 := 0;

Task/Totient-function/EasyLang/totient-function.easy

@@ -0,0 +1,40 @@
+func totient n .
+   tot = n
+   i = 2
+   while i <= sqrt n
+      if n mod i = 0
+         while n mod i = 0
+            n = n div i
+         .
+         tot -= tot div i
+      .
+      if i = 2
+         i = 1
+      .
+      i += 2
+   .
+   if n > 1
+      tot -= tot div n
+   .
+   return tot
+.
+numfmt 0 3
+print "  N Prim Phi"
+for n = 1 to 25
+   tot = totient n
+   x$ = "    "
+   if n - 1 = tot
+      x$ = " x  "
+   .
+   print n & x$ & tot
+.
+print ""
+for n = 1 to 100000
+   tot = totient n
+   if n - 1 = tot
+      cnt += 1
+   .
+   if n = 100 or n = 1000 or n = 10000 or n = 100000
+      print n & " - " & cnt & " primes"
+   .
+.

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

Task/Totient-function/Quackery/totient-function.quackery

@@ -1,8 +1,3 @@
-  [ [ dup while
-      tuck mod again ]
-    drop abs ]              is gcd        ( n n --> n )
-
-
   [ 0 swap dup times
       [ i over gcd
         1 = rot + swap ]